List of top Mathematics Questions on Integration

The value of \(\displaystyle\int_{0}^{\pi/4}\sin^{3}2x\cos2x\,dx\) is:

The value of \(\displaystyle\int_{2}^{2\sqrt3}\frac{dx}{4+x^{2}}\) is:

Evaluate: \(\displaystyle\int_0^\pi \frac{x\,dx}{a^2\cos^2x+b^2\sin^2x}\)

Evaluate: \(\displaystyle\int_0^1 \frac{\tan^{-1}x}{1+x^2}\, dx\)

Solve: \(\displaystyle\int \cos^2 x\, dx\)

The value of \(\displaystyle\int_0^{2/3} \frac{dx}{4+9x^2}\) is:

Evaluate: \(\displaystyle\int_{-\pi/2}^{\pi/2} (x^3 + x\cos x)\, dx\)

Find the value of \(\displaystyle\int\left(\sqrt{\cot x}+\sqrt{\tan x}\right)dx\).

Prove that \(\displaystyle\int_0^{\pi/2}\log\sin x\,dx=-\dfrac{\pi}{2}\log2\).

Evaluate: \(\displaystyle\int\dfrac{1}{\sqrt{2x-x^2}}\,dx\).

Integrate \(x\log x\) with respect to \(x\).

The value of the integral \(\displaystyle\int\dfrac{\sin^2x-\cos^2x}{\sin^2x\cos^2x}\,dx\) is

Solve: \(\displaystyle\int\left[\sqrt{\cot x}+\sqrt{\tan x}\right]dx\).

Evaluate \(\displaystyle\int\dfrac{x^2+1}{x^2-5x+6}\,dx\).

The value of \(\displaystyle\int x\cos x\,dx\) is:

Find the value of the integral \(\displaystyle\int\dfrac{x^{4}}{(x-1)(x^{2}+1)}\,dx\).

Find the value of \(\displaystyle\int_{1}^{4}\big(|x-1|+|x-2|+|x-3|\big)\,dx\).

Find the value of \(\displaystyle\int_{-1}^{2}|x^{3}-x|\,dx\).

Find \(\displaystyle\int\left[\sqrt{\tan x}+\sqrt{\cot x}\right]dx\).

Find \(\displaystyle\int\dfrac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx\).

Find \(\displaystyle\int e^x\left(\dfrac{1+\sin x}{1+\cos x}\right)dx\).

Find the value of the integral \(\displaystyle\int x^2\tan(x^3+2)\,dx\).

The value of \( \displaystyle \int_{0}^{\pi/2} \frac{dx}{1 + \sqrt{\tan x}} \) will be

Find ∫ dx / (sin²x cos²x)