List of top Mathematics Questions on Integration

The value of \( \int_{-\pi/2}^{\pi/2} \frac{dx}{[x]+4} \) is, where [.] denotes greatest integer function:

Evaluate the integral: \[ \int \frac{\sqrt{\tan x}}{\sin x \cos x} \, dx \]

The integration of $\log x$ with respect to $x$ is

$\int \frac{1}{(2\cos x + \sin x)^2} dx =$

$\int x\text{Tan}^{-1}\sqrt{\frac{1+x^2}{1-x^2}}dx=$

Evaluate the integral: $ \int \frac{1}{x(x^4 + 1)} \, dx $

Evaluate the integral: \[ \int e^x \sec(x) \left( \tan(x) + 1 \right) \, dx \]

Evaluate the integral: \[ \int \frac{\sin^1 x}{\sqrt{1 - x^2}} \, dx \]

Evaluate the integral: \[ \int_{\frac{\pi}{10}}^{\frac{2\pi}{5}} \frac{\cot^3 x}{1 + \cot^3 x} \, dx \]

Evaluate the integral: \[ \int \frac{2x^2 + 4x + 3}{x^2 + x + 1} \, dx \]

Evaluate the integral: $ \int \frac{\sec^2(\sqrt{2x+5})}{\sqrt{2x+5}} \, dx $

Evaluate the integral: $ \int e^{-x} \cdot e^{3x} \, dx $

Evaluate the integral $ I = \int \frac{\sin 4x}{\sin 2x} \, dx $

Evaluate the integral: $ \int_0^\pi \frac{\tan x}{\cos x} \, dx = \int_0^\pi \frac{\sin x}{\cos^2 x} \, dx $

Evaluate the integral: $ \int_{-1}^1 |x - 3| \, dx $

Evaluate the integral: $ \int e^{x + \frac{1}{x}} \frac{x^2 - 1}{x^2} \, dx $

Evaluate the following integral: $ \int e^{2\theta} \left( 2 \cos^2 \theta - \sin 2\theta \right) \, d\theta $

Evaluate the integral: $ \int_0^{\frac{\pi}{2}} \frac{1}{1 + \sin x} \, dx $

Evaluate the following integral: $ \int \frac{\sec x}{(\sec x + \tan x)^2} \, dx $

Evaluate the integral: $ \int \frac{1}{x(x^4 + 1)} \, dx $

Evaluate the integral: $ \int \frac{1}{x(x^4 + 1)} \, dx $

If $\int_0^{\pi/2}\tan^{14}(x/2)dx = 2\left[\sum_{n=1}^7 f(n) - \frac{\pi}{4}\right]$, then $f(n)=$

The area of the region bounded by $y=x^3$, x-axis, $x=-2$ and $x=4$ is