I know you tried very hard to answer all the
Integration by Substitution problems. It's time to check your works and see how well are you in solving the integrals using the u-substitution method.
Integration by substitution with algebraic functions
1.
2.
3.
4.
5.
Integration by substitution involving exponential functions
1.
2.
3.
4.
5.
Integration by substitution involving trigonometric functions
1.
+ C
2.
3.
4.
5.
Algebraic substitution involving integral giving inverse trigonometric functions
1.
+ C
2.
3.
4.
5.
Review Integration by Substitution
In case you want to review the the
Integration by substitution lectures to fully understand how this method works. Kindly follow the link above.
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Integral Calculus
![solution for Integral of arctanx dx limit[0,1]](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjs6AMCYoBN9ENCBXiN3IzC2a_Eh8UVGw7hdbJP1PN9yRur27pb6NQyZazfqbhNR2VmmjtJD3vxgA2btQebpKalUJEwXPSfnI16VMEV-LvKAWLg6vJgzWKtqSUqTqCGYFr2AyjMxtyiflg/s600/solution-integral-arctanxdx.gif "answer for Integral of arctanx dx limit[0,1]"){kind=small}
![solution for the integral of (5x+1)/[(2x+1)(x-1)] dx](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_u-nY5IgldM-msvM7GhGrygWu1GWSorJheSDrMEIyZJ_L2r9SlSgaUxtMnsodiGnm9GXCfWlvaA-Lsp1brb796K-U9z9EGURLGnxbYHP31VfV0H2ZSLOn5C1P_J-qUAiXNz7L-MgmDs3FEGZsezzewAtwA29euekAaGqcRtkvTvEEnbTRSzCHRFkGa0NFCouxeH7PozNfMCEn29iUg8=s0-d "answer for the integral of (5x+1)/[(2x+1)(x-1)] dx"){kind=small}
![solution for the integral of [(x^3-2x^2-4)/x^3-2x^2] dx](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_txg6KCjoHGK2E7vYsjnT-3JmBptyKBcNdYAMUor1W0KbPptV3_-iGhrSWrWVFVXMbU6X1IUa4VXJT1B1jctLAdnkXSphbiRt7eFSOZfWjjO_mYxdRfjrln0q9VPiUoKiAQTyrdbAJYvMvFlLbY3WsA_71anqFS6sTbaY4RSGW4PqBTAw1Ug7lI5thXoo3WVg5IIWrsyQ1MgV4=s0-d "answer for the integral of [(x^3-2x^2-4)/x^3-2x^2] dx"){kind=small}
![solution for the integral of [x^2+1/(x-3)(x-2)^2] dx](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uJu53cIr-V74VGytEKN270Z45CBmDvujWFQzEgv2cwb_1YtUWfaoGclVXCM_hIgzBuzeDOlDoQZatwQpL-eopiwpJY681SzluaPNFW-ucbJ6t4ypDFIcBgZFJysdiIBxNDzHn9jWYvpIr5oGZT2gijOtJTYbHfTrCrZlRwWX41nXZKQASJYhgeRulA4U6onyL1tE8LG1z4bRwfqXCv0kw=s0-d "answer for the integral of [x^2+1/(x-3)(x-2)^2] dx"){kind=small}
![solution for the integral of [(x^3+4)/(x^2+4)] dx](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vKb5AKWLSGdPUfZ0uh3NSDbnpzeukpRQXYq3bfzPqikPN0V5-wEWp-LY5iFRWXBkqBgCEYak6DISOKB1Ki9946oryJL1xUPFhnBL04AN2BEs6GnVLm9t3Il8yjHbBfL63AftDI5aPPPcrrvhCAJ66m4Jlb3kYvobqnvkoOdVUkTMbc7RoxRydkmVqK3qJ3bPHGrWWF-FVN27tmoOgaEOSvmXhRY0f57-bIurtFyxv32b8IiJ2e7sh9UHirLs6Gamy1K3hN6dPRPcFkrmr4vUSEBMiq2OoUsSDvxYuktj6wrb_NVPNRgX8WC1K3y6olCYM=s0-d "answer for the integral of [(x^3+4)/(x^2+4)] dx"){kind=small}
![solution for the integral of [10/(x-1)(x^2+9)] dx](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vxzqq8fOevBzt2fU22OxGdAdqWapC-UKcjkCEsCzR3m3b67atTlPhvJvVFiHE3p0L3UakT4eACDBPzbf1O-_HT3H9i-fD9LezDCTOIZYwf-t7Oud5xHeTbR2QjEhL8Rk9Ew9pcM0kceW_XWxj4K8fRfTinuMV_VhhJAM5BjFAjTRyl52_6UeSTDo8lzXwwUo4PI17rlfiKdXZl-E2JuvRyirDKE7rGF17t2E2OXJ_OBJ4xtJGKvnvUxTiceuKi4xhkcLuGfO6w0azpFcRU9kMnNxs42aZzBnii-EKifm4EezLxjnpHJCBgmSql3a8D3IkBFJlFB_0INbNVoqcNHAZoIvOO7T0=s0-d "answer for the integral of [10/(x-1)(x^2+9)] dx"){kind=small}
![solution for the integral of [4x/(x^3+x^2+x+1)] dx](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tb5fCEPdCad7aiW_Oe7Q_jNJivgf3n9bvw4tLWpVajgwKsEbYzIhsRr0-_vmMxJld39l7v33C_9qgulrLF17TobhAIzlPxQyUWuzSRAQfk7g1VR_JsIXiDLMKP0eRVbV6E0F0VnefLSeyMW9JQyQ0ExhQ-VlAiOhbpwi2t-i7MoplAqSDUHDzmQH713iPkrZ4cJJAl7HOFauB3IBFU3tBoxaWqT_Ppior4wnzaDLY=s0-d "answer for the integral of [4x/(x^3+x^2+x+1)] dx"){kind=small}
![solution for the integral of [(x^3+x^2+2x+1)/(x^2+1)(x^2+2)] dx](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_sWtFvjwGYATsSPMhkR9SVF9-jZ4NIngS98W5qKvTULRf3_Ad2VCFO6-Utd5MWdaFCq0T85Ix5t7XLNYyUXn1tuXpJYlbkrV7vifgnfM0ROoRd1yKCRrBnFqBuwoRbfedVooBjSEAUWbQdjcMdcpnPpCP1CR7tbsv-yV6TMBWHs8S5FQ34obuPPXIUPuFVtVSZ0qEr5ffJFbBt5zUNr-yC0lHJZ7nXDemSXHzr75qdrdqRUAtKi1IcIHqG6OOE7It1-a6cmNgHA-zVOuiQ7a9P0ZiWaXarWGwLv4x0IhyB21W5zgnv5aIbn2KwPMP6VWSGPnVBazFs9lpS35BrUFoB9Ex0orIFfjZ5pnEk_fFbZZZUTHFMFlVYOVp5-qsOnftK1=s0-d "answer for the integral of [(x^3+x^2+2x+1)/(x^2+1)(x^2+2)] dx"){kind=small}
![solution for the integral of [(x+4)/(x^2+2x+5)] dx](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tS_MhGE2-Ey9z_rrXKa-rJAEDQYi8pYaqXkbbjVegT6pgJGNNdp-4PwIL4QX_wkD_CstEXHisPqtR7KyAXj7m_WxeEC6fQnc__POdOp632pX_VA5TWPfmPOzKoZLi66eSR2aSpt-sDfL5kS5tCvjx2KbhKnepFVCQdtsHpJipErPPyrRvsu5w2U9kuZeU_0B3TMxLwSYotc7Z5MYe5d1fk-K8eVjtEsSp6dMSKmTDlaomMAljTu7L_sgO2dA89Osx-upVVEm20oFM8oa4GU8W7xMF0uUxRRhS6Cl7xT8G7wGdcOb0YGw5ETilsAjUbMuyu5zANlVuoSnWD=s0-d "answer the integral of [(x+4)/(x^2+2x+5)] dx"){kind=small}
![solution for the integral of [1/(x^3-1)] dx](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vzRHOjW5FUqmermVvvGzT8QHPKzNVlh1T1oScUVaqtgiuJgw6oTqRrSy7zau36CIfb02oen9bH0Bw1zMdBCGM1ljjVKbtnLQso4RUyR98OeS0Sa4EJUwj09oasvHpbN3v-sOdnDRU0tti598fKXsrsGDDkG0qQTckCPM-HFroSwm6RDiaaPu50c8ngBEHVD6GVskx__BnhoNNF7YWPbTB3Bst6JUz_v1IDEdNgDDFP9cuHIrJ0-8keDBs_W99QejNOyjBJrT7UuLOIvFfe1nWKOr9ST7JXy1vy_R3PWdqL2C0Seq_cq8D_p7eFoeb1immnvs90r8clabR3_njozBfIczSHHcUGOW0EeLHoGHAb1fWNfLCA8Df6lTx-4BM8BoriA8UhaShIa2FESqoQkOTRibxB9on3pWAC0iTTobFre6wqdYWHBU5GbV4i_D5706u7-yzZ=s0-d "answer for the integral of [1/(x^3-1)] dx"){kind=small}
![solution for the integral of [1/(x(x^2+4)^2)] dx](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_sCTxwgJEpTEzHM1y_hTZnz2k_uNiAr6bOenYzoG5aBZa1sbKXU8X5stDphNZXPGSLElSdKKG2sGLjc7RdijVPt57uMgRM0fWT7qOz8Hk4sIVtwMXJ_a1ugqNf-AdmZFOx4PuDuZ-DjHq1Ad1DX7jvDPLeax6Pdmi9qmUddb-xkLhrsgW5RCJDUFDolQAdn1AGgb3qzhVnp5mENIErh8_TFq2IeatpKRhqfkh44mn6QTk5FYavkLFbf8jCypz3OQtIkRweg7C0e-5lW1_DpyN3dSzlSDz8Yb5xzS3Phpj3qvtKgvyxnfwi2DkzIhB0YLht0R4SDmTSo1qcDAyi8h6exibNiQA=s0-d "answer for the integral of [1/(x(x^2+4)^2)] dx"){kind=small}
![solution for the integral of [(x^2-3x+7)/(x^2-4x+6)^2] dx](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tINmrEQ682MLKMXKXVQ6dXDxxSwvLmgJ7eA_G6yFR7n8PVH5sYX-w8vSTgdXDGSNgWToRh5xlPVfjGSMb6gQxJ4l9X7uaQawXd2MNshIZ0OxkKvZ3TsPl2JvT8RDQIQCRaiNiqCWDNiFEUIjp-FUo9TMYCUIOPlj077TTlVCPVLRBypGImq0R4UisPh_zte17dhSgXf-0PeMtpzPTIwfXbmGqS8Ofh5gq3dQBlELRIZ-LK-URHlfcpVzhmiiU_vBARQlijwwK41FPP1F25g8GQ--q3ydBjS_xhK1p_SD1vFRY75ZDBkUwfUYUUmEJHbwh22nD4CJipg6Mbecqtq14lPx3ZYYZFG91QpbDs1VZh8eR2mfTdycNzBD6le5fTdVaA6rcSxUU=s0-d "answer for the integral of [(x^2-3x+7)/(x^2-4x+6)^2] dx"){kind=small}
![solution for the integral of [1/(x^5+2x^3+x)] dx](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_sa97V0dRwUxNJoU7DUZysO3bSHcZ0qdJSLSvcgvxl6ea7pXcT1E9A5t_xwVeovxUuNYddhjUBm6YB4d_6pAkdp5EpAFbEKWdQCHl50Cbzs45yh4SV-0p_-Opdy9lV6AEQJRmQ_QZLzNEMKWcWopKruWX4u4fp6wfTAz4BvlDNxAmMj-7dPKaxEAzn0yFqnCKaHnQ00KT3l8kD03QMWIIPrQfjPzvHBqkMFwMvp4cf5_KSx5Yv5oDVucLtOTIl1btLU_9tsW7iNObBofjOCqYkEyG6meY0u0F2AxZcyUAlm1u7e=s0-d "answer for the integral of [1/(x^5+2x^3+x)] dx"){kind=small}
