# Integration by Substitution

1. $${\ }e^{4x}$$
2. $${\ }8xe^{x^{2}+7}$$
3. $${\ }4xe^{2x}\sqrt{x^{3}+3}$$
4. $${\ }4x\sqrt{x^{2}+8}$$
5. $${\ }xe^{x^{2}}$$
6. $${\ }\frac{4x\; -\; 6}{x^{2}-\; 3x+\; 7}$$
7. $${\ }\frac{3x^{5}\; +\; 1}{x^{6}+\; 2x}$$
8. $${\ }\frac{2ax\; +\; b}{\left( ax^{2}+bx+c \right)^{2}}$$
9. $${\ }\frac{2x}{\sqrt{x^{2}+4}}$$
10. $${\ }\frac{12x+8}{3x^{2}+4x+8}$$
11. $${\ }\frac{\left( \log x \right)^{3}}{x}$$
12. $${\ }\frac{x}{\left( x^{2}+a^{2} \right)^{n}}$$
13. $${\ }\int_{}^{}{\left( 7e^{2x}+\; \frac{5}{2x\; +\; 7}\; -2\; \sqrt{1-\; 5x} \right)}dx$$
14. $${\ }\int_{}^{}{\left( Ax\; +\; B \right)^{n}}dx$$
15. $${\ }\int_{}^{}{x^{2}e^{x^{3}}}dx$$
16. $${\ }\int_{}^{}{x^{3}\sqrt{x^{2}-3}} dx$$
17. $${\ }\int_{}^{}{x^{4}\; e^{x^{5}}}dx$$
18. $${\ }\int_{}^{}{3x^{2}\; \left( x^{3}\; +\; 5 \right)^{4}}dx$$
19. $${\ }\int_{}^{}{x^{n-1}\; \left( 5\; +\; 7x^{n} \right)^{}}dx$$
20. $${\ }\int_{}^{}{e^{x}\; \left( e^{x}+2 \right)^{2}}dx$$
21. $${\ }\int_{}^{}{x\sqrt{2x^{2}+3}}dx$$
22. $${\ }\int_{}^{}{\frac{x^{n-1}}{\left( a+bx^{n} \right)^{n}}}dx$$
23. $${\ }\int_{}^{}{\frac{x}{x^{2}+a^{2}}}\; dx$$
24. $${\ }\int_{}^{}{\frac{x^{2}\; -\; x}{x^{3}-\; 3x\; +2}}\; dx$$
25. $${\ }\int_{}^{}{\frac{1}{x}e^{\log x}}\; dx$$
26. $${\ }\int_{}^{}{\frac{1}{x}\left( \log x \right)^{2}e^{\left( \log x \right)^{3}}}\; dx$$
27. $${\ }\int_{}^{}{}\frac{dx}{x+\sqrt{x}}$$
28. $${\ }\int_{}^{}{\frac{\left( x+1 \right)\; \left( x+\; \log x \right)^{2}}{x}}dx$$
29. $${\ }\int_{}^{}{\frac{x}{\sqrt{2x^{2}+3}}}dx$$
30. $${\ }\int_{}^{}{\frac{x^{2}}{\sqrt{1-x}}}dx$$
3 Responses to “Integration by Substitution”
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