List of top Mathematics Questions on Integration asked in KCET

If 'n' is a natural number, then $\int \frac{\sin^n x}{\cos^{n+2} x} dx =$

$\int e^{-x \log 2} 2^x dx =$

The value of \( \int \frac{dx}{(x+1)(x+2)} \) is:

The value of \( \int_{-1}^1 \sin^5 x \cos^4 x \, dx \) is:

The integral \[ \int \frac{dx}{x^2 \left( x^4 + 1 \right)^{3/4}} \] equals:

The value of the integral \[ \int_0^1 \log(1 - x) \, dx \] is:

If $y = 2x^{3x}$, then $\frac{dy}{dx}$ at $x = 1$ is:

$\frac{d}{dx} \left[ \cos^2 \left( \cot^{-1} \sqrt{\frac{2 + x}{2 - x}} \right) \right]$ is:}

$\int \frac{\sin x}{3 + 4\cos^2 x} \, dx =$

$\int_{-\pi}^\pi (1 - x^2)\sin x \cos^2 x \, dx =$

$\int \frac{1}{x \left(6(\log x)^2 + 7\log x + 2\right)} \, dx =$

$\int \frac{\sin \frac{5x}{2}}{\sin \frac{x}{2}} \, dx =$

$\int_{1}^{5} \left(|x - 3| + |1 - x|\right) \, dx =$

The solution of $e^{\frac{dy}{dx}} = x + 1, \, y(0) = 3$ is:

\(\int\limits_1^5(|x-3|+|1-x|)dx\)=