1. $\displaystyle \displaystyle\int{{{x}^{2}}{{({{x}^{3}}+3)}^{3}}}\,\mathrm{d}x$ 2. \(\displaysty

Question

1. $\displaystyle \displaystyle\int{{{x}^{2}}{{({{x}^{3}}+3)}^{3}}}\,\mathrm{d}x$ 2. $\displaystyle \displaystyle\int{(5{{x}^{4}}+4x)({{x}^{5}}+2{{x}^{2}}}+1{{)}^{3}}\,\mathrm{d}x$ 3. $\displaystyle \displaystyle\int{\frac{3x-2}{{{\left( 3{{x}^{2}}-4x-1 \right)}^{3}}}}\,\mathrm{d}x$ 4. $\displaystyle \displaystyle\int{\frac{{{x}^{2}}}{\sqrt{{{x}^{3}}+1}}\,\mathrm{d}x}$ 5. $\displaystyle \displaystyle\int{\frac{21{{x}^{2}}+14}{\sqrt{{{x}^{3}}+2x+1}}\,\mathrm{d}x}$ 6. $\displaystyle \displaystyle\int{\frac{x}{{{\sqrt{1-2{{x}^{2}}}}^{5}}}\,\mathrm{d}x}$ 7. $\displaystyle \displaystyle\int{{{\left( \frac{x}{\sqrt{3{{x}^{4}}-1}} \right)}^{3}}\,\mathrm{d}x}$ 8. $\displaystyle \displaystyle\int{3{{x}^{3}}{{(2{{x}^{4}}-5)}^{8}}}\,\mathrm{d}x$ 9. $\displaystyle \displaystyle\int{{{e}^{3x}}{{({{e}^{3x}}+5)}^{11}}}\,\mathrm{d}x$ 10. $\displaystyle \displaystyle\int{\frac{{{x}^{3}}}{{{x}^{4}}+3}\text{ }}\mathrm{d}x$ 11. $\displaystyle \displaystyle\int{\frac{2x+1}{\left( 2{{x}^{2}}+2x+5 \right)}}\,\mathrm{d}x$ 12. $\displaystyle \displaystyle\int{\frac{3x}{1+{{x}^{2}}}}\,\mathrm{d}x$ 13. $\displaystyle \displaystyle\int{\frac{2x+1}{{{x}^{2}}+x+1}}\,\mathrm{d}x$ 14. $\displaystyle \displaystyle\int{\frac{1}{\sqrt{x}{{(\sqrt{x}+1)}^{9}}}}\,\mathrm{d}x$ 15. $\displaystyle \displaystyle\int{\frac{1}{\sqrt{x}{{e}^{\sqrt{x}}}}}\,\mathrm{d}x$ 16. $\displaystyle \displaystyle\int{\frac{{{\left( \ln x \right)}^{8}}}{x}}\,\mathrm{d}x$ 17. $\displaystyle \displaystyle\int{\frac{1}{x\ln {{x}^{3}}}}\,\mathrm{d}x$ 18. $\displaystyle \displaystyle\int{x}\left( {{e}^{{{x}^{2}}+3}} \right)\,\mathrm{d}x$ 19. $\displaystyle \displaystyle\int{x{{e}^{{{x}^{2}}}}}\left( {{e}^{{{x}^{2}}-1}} \right)\,\mathrm{d}x$ 20. $\displaystyle \displaystyle\int{\frac{1}{1+{{e}^{-x}}}}\,\mathrm{d}x$ 21. $\displaystyle \displaystyle\int{{{x}^{7}}\cos ({{x}^{8}}+2)}\,\mathrm{d}x$ 22. $\displaystyle \displaystyle\int{\tan 3x}\,\mathrm{d}x$ 23. $\displaystyle \displaystyle\int{\cot x}\,\mathrm{d}x$ 24. $\displaystyle \displaystyle\int{\frac{{{\tan }^{5}}x}{{{\cos }^{2}}x}}\,\mathrm{d}x$ 25. $\displaystyle \displaystyle\int{\frac{1}{{{\sin }^{2}}x\tan x}}\,\mathrm{d}x$ 26. $\displaystyle \displaystyle\int{\sec x\tan x}\,\mathrm{d}x$ 27. $\displaystyle \displaystyle\int{\text{cosec }x\cot x}\,\mathrm{d}x$ 28. $\displaystyle \displaystyle\int{\frac{\sin x\cos x}{{{\sin }^{2}}x+7{{\cos }^{2}}x}}\,\mathrm{d}x$ 29. $\displaystyle \displaystyle\int{\frac{\sin 2x}{\sqrt{5{{\sin }^{2}}x+4{{\cos }^{2}}x}}}\,\mathrm{d}x$ 30. $\displaystyle \displaystyle\int{(\sin x){{e}^{\cos x}}}\,\mathrm{d}x$ 31. $\displaystyle \displaystyle\int{x{{e}^{{{x}^{2}}}}}\,\mathrm{d}x$ 32. $\displaystyle \displaystyle\int{{{2}^{x}}}\,\mathrm{d}x$ 33. $\displaystyle \displaystyle\int{{{5}^{x}}}\,\mathrm{d}x$

Accepted Answer

1. $\frac{{{({{x}^{3}}+3)}^{4}}}{12}+C$ 2. $\frac{{{({{x}^{5}}+2{{x}^{2}}+1)}^{4}}}{4}+C$ 3. $-\frac{1}{4{{\left( 3{{x}^{2}}-4x-1 ight)}^{2}}}+C$ 4. $\frac{2}{3}\sqrt{{{x}^{3}}+1}+C$ 5. $14\sqrt{{{x}^{3}}+2x+1}+C$ 6. $\frac{1}{6{{\sqrt{1-2{{x}^{2}}}}^{3}}}+C$ 7. $-\frac{1}{6\sqrt{3{{x}^{4}}-1}}+C$ 8. $\frac{{{(2{{x}^{4}}-5)}^{9}}}{24}+C$ 9. $\frac{{{({{e}^{3x}}+5)}^{12}}}{36}+C$ 10. $\frac{1}{4}\ln \left| {{x}^{4}}+3 ight|+C$ 11. $\frac{\ln \left| 2{{x}^{2}}+2x+5 ight|}{2}+C$ 12. $\frac{1}{2}\ln \left| 1+{{x}^{2}} ight|+C$ 13. $\ln \left| {{x}^{2}}+x+1 ight|+C$ 14. $-\frac{1}{4{{(\sqrt{x}+1)}^{8}}}+C$ 15. $-2{{e}^{-\sqrt{x}}}+C$ 16. $\frac{{{\left( \ln x ight)}^{9}}}{9}+C$ 17. $\frac{1}{3}\ln \left| \ln \left| x ight| ight|+C$ 18. $\frac{{{e}^{{{x}^{2}}+3}}}{2}+C$ 19. $\frac{1}{4}\left( {{e}^{2{{x}^{2}}-1}} ight)+C$ 20. $\ln \left| {{e}^{x}}+1 ight|+C$ 21. $\frac{1}{8}\sin \left( {{x}^{8}}+2 ight)+C$ 22. $\frac{1}{3}\ln \left| \sec 3x ight|+C$ 23. $\ln \left| \sin x ight|+C$ 24. $\frac{{{	an }^{6}}x}{6}+C$ 25. $-\frac{{{\cot }^{2}}x}{2}+C$ 26. $\sec x+C$ 27. $-	ext{cosec }x+C$ 28. $-\frac{1}{12}\ln \left| {{\sin }^{2}}x+7{{\cos }^{2}}x ight|+C$ 29. $2\sqrt{5{{\sin }^{2}}x+4{{\cos }^{2}}x}+C$ 30. $-{{e}^{\cos x}}+C$ 31. $\frac{1}{2}{{e}^{{{x}^{2}}}}+C$ 32. $\frac{{{2}^{x}}}{\ln 2}+C$ 33. $\frac{{{5}^{x}}}{\ln 5}+C$

Techniques of Integration - Cancelling Method of MF 26 Integrals

Techniques of Integration - Cancelling Method of MF 26 Integrals