List of top Mathematics Questions on Indefinite Integrals asked in Bihar Board XII

Evaluate the integral: \[ \int x e^x \, dx \] The correct answer is:
Evaluate the integral: \[ \int \frac{1 + x^8}{x^3} \, dx \] The correct answer is:
Evaluate the integral: \[ \int \frac{2}{2 - 3x} \, dx \] The correct answer is:
Evaluate the integral: \[ \int \sec x \, dx \] The correct answer is:
Evaluate the integral: \[ \int \tan^2 x \, dx \] The correct answer is:
Evaluate the integral: \[ \int \frac{1 + \cos(2x)}{1 - \cos(2x)} \, dx \] The correct answer is:
Evaluate the integral: \[ \int \sec^5 x \tan x \, dx \] The correct answer is:
Evaluate the integral: \[ \int \cos^2 x \cdot \sin^2 x \, dx \] The correct answer is:
Evaluate the integral: \[ \int \frac{x^2 + 1}{x^4 + 1} \, dx \] The correct answer is:
Evaluate the integral: \[ \int \frac{dx}{a^2 + x^2} \] The correct answer is:
\(\displaystyle \int \sin^{3}\theta\ \csc^{2}\theta\,d\theta=\ \ ?\)
\(\displaystyle \int \big(\cos\theta\,\csc^{2}\theta-\cos\theta\,\cot^{2}\theta\big)\,d\theta=\ \ ?\)
\(\displaystyle \int (4\cos x-5\sin x)\,dx=\ \ ?\)
\(\displaystyle \int \frac{3\cos x-2\sin x}{2\cos x+3\sin x}\,dx=\ \ ?\)
\(\displaystyle \int \frac{3x^{2}+2}{x^{3}+2x}\,dx=\ \ ?\)
\(\displaystyle \int \frac{dx}{x^{2}+5}=\ \ ?\)

\(\displaystyle \int \sin\!\left(\frac{3x}{4}\right)\,dx=\) ?

\(\displaystyle \int \cos\!\left(\frac{7x}{9}\right)\,dx=\) ?

\(\displaystyle \int \sec^{2}\!\left(\frac{17x}{23}\right)\,dx=\) ?

\(\displaystyle \int 4^{x}\,dx=\) ?

\(\displaystyle \int x\,(4x^{2}-6)\,dx=\) ?

\(\displaystyle \int e^{x}(\cos x-\sin x)\,dx=\) ?

\(\displaystyle \int e^{x}\,(x^{3}+3x^{2})\,dx=\) ?

\(\displaystyle \int e^{x}\!\left(\frac{1}{x}-\frac{1}{x^{2}}\right)\,dx=\) ?

\(3\displaystyle \int \sqrt{x}\,dx=\) ?