Indefinite Integration: JEE Main Mathematics Previous Year Questions

459 previous year questions from Indefinite Integration. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. 1.If $\int \frac{\sqrt{1-x^4}}{x^7}\text{dx}=f\text{(}x\text{)}{\left(\sqrt{1-x^4}\right)}^n+C$, then $\text{(}f\text{(}x\text{)}{\text{)}}^n$ is equal to
2. 2.$\sum \frac{\text{cos}\text{⁡}7x-\text{cos}\text{⁡}8x}{1+2\text{cos}\text{⁡}5x}\text{dx}=$
3. 3.If…
4. 4.If $x\ne 1$ and $\sum \frac{(x^3+x^2-x-1)}{(x^5+x^4+3x^3+3x^2+x+1){\text{tan}}^{-1}\text{⁡}\left(\frac{x^2+1}{x}\right)}dx$…
5. 5.$\sum \sqrt{4{\text{cos}}^2\text{⁡}x-5{\text{sin}}^2\text{⁡}x}\text{cos}\text{xdx}=$
6. 6.If $\int \frac{\text{dx}}{{\text{cos}}^4\text{⁡}x+{\text{sin}}^4\text{⁡}x}=\frac{1}{\sqrt{2}}{\text{tan}}^{-1}\text{⁡}\text{[}g\text{(}x\text{)}\text{]}+C$, then…
7. 7.${\int }_1^2\frac{x^3-1}{x^2}\text{dx}$ is equal to
8. 8.If $\int \frac{{\text{sin}}^2\text{⁡}\alpha -{\text{sin}}^2\text{⁡}x}{\text{cos}\text{⁡}x-\text{cos}\text{⁡}\alpha }\text{dx}=f\text{(}x\text{)}+\text{Ax}+B$ and…
9. 9.$\int \frac{{\text{cos}}^{n-1}\text{⁡}x}{{\text{sin}}^{n+1}\text{⁡}x}\text{dx}\text{,}n\ne 0$ is
10. 10.The value of $\int e^{\text{sin}\text{⁡}x}\text{sin}\text{⁡}2\text{xdx}$ is
11. 11.Let $f\text{(}x\text{)}=\int \frac{e^{3x}}{4+8e^{2x}+e^{4x}}\text{dx}$ and $g\text{(}x\text{)}=\int \frac{2\text{dx}}{e^{3x}+8e^x+4e^{-x}}\text{dx}$, then…
12. 12.$\int \frac{{\sec }^{2}x}{(\sec x+\tan x{)}^2}dx=$
13. 13.$\int 3^{-{\text{log}}_9\text{⁡}{x}^2}\text{dx}=$
14. 14.The value of ${\int }_0^1\frac{\text{log}\text{⁡}\text{(}1+x\text{)}}{1+x^2}\text{dx}$ is
15. 15.$\text{lim}n\to \infty \frac{1}{n}(\frac{1}{e^{1/n}}+\frac{1}{e^{2/n}}+\frac{1}{e^{3/n}}+\text{…}+\frac{1}{e^2})=$
16. 16.If $\int \frac{x+1}{\sqrt{2x-1}}dx=f\text{(}x\text{)}\sqrt{2x-1}+C$ where $C$ is a constant of integration, then $f\text{(}x\text{)}$ is equal to:
17. 17.It is given that $\frac{d}{\text{dt}}\text{(}\text{tlog}\text{⁡}t-t\text{)}=\text{log}\text{⁡}t$ then…
18. 18.${\int }_1^4(x+\sqrt{x}+\frac{1}{x})\text{dx}-{\int }_1^{2\text{log}\text{⁡}2}\text{dx}=$
19. 19.The integral $\int \text{cos}\text{⁡}\left({\text{log}}_{e}x\right)\text{dx}$ is equal to : (where $C$ is a constant of integration)
20. 20.If…
21. 21.$\frac{x^4}{(x^2+1)(x^2+3)}=$
22. 22.${\int }_{-1}^1\frac{\sqrt{1+x+x^2}-\sqrt{1-x+x^2}}{\sqrt{1+x+x^2}+\sqrt{1-x+x^2}}\text{dx}$ is equal to
23. 23.$\sum \frac{e^{\text{cot}\text{⁡}x}}{{\text{sin}}^2\text{⁡}x}\text{(}2\text{log}\text{⁡}\text{cosec}\text{⁡}x+\text{sin}\text{⁡}2x\text{)}\text{dx}=$
24. 24.If $\int \frac{\text{dx}}{x\left(\sqrt{x^4-1}\right)}=\frac{1}{k}{\text{sec}}^{-1}\text{⁡}\left(x^k\right)$, then the value of $k$ is equal to
25. 25.${\int }_{-2}^2\text{|}x\text{cos}\text{⁡}\text{πx}\text{|}\text{dx}$ is equal to