List of top Mathematics Questions on Integration asked in KEAM

$\int x(1+2\log x)dx$ is equal to

$\int\frac{x\cos x-\sin x}{x^{2}}dx$ is equal to

$\int\frac{2+3x}{2\sqrt{1+x}}dx$ is equal to} \textit{Note: The original exam paper contained a typographical error in the denominator ($1+c$ instead of $1+x$). It has been corrected here to match the given solutions.

$\int\frac{\tan x+\cot x}{1+\tan^{2}x}dx$ is equal to

$\int e^{-x}(1+(1-x)\log x)dx$ is equal to

$\int\left(\frac{1}{1+e^{t}}\right)dt$ is equal to

$\int\frac{1}{(1+x^{2})\tan^{-1}\left(\frac{1+x}{1-x}\right)}dx$ is equal to

$\int e^{x}(2e^{x}+\sin x+\cos x+2)dx$ is equal to

$\int\frac{y^{2}-3y+2}{y^{2}+y}dy$ is equal to

$\int \tan\frac{\theta}{2}\sin\theta\cos\theta\, d\theta$ is equal to

Evaluate the integral: \[ \int_0^1 \frac{t}{(t + 1)^3} \, dt \]

Evaluate the integral: \[ \int 16x^3 \log_e x \, dx \]

Evaluate the integral: \[ \int \left( 27x^3 (1 - x^3)^{\frac{1}{3}} \right) dx \]

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

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

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

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

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

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

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

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

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

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