List of top Mathematics Questions on Methods of Integration asked in MHT CET

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

If $\int \frac{2x+3}{(x-1)(x^2+1)} dx = \log_e \left\{ (x - 1)^{\frac{5}{2}} (x^2 + 1)^a \right\} - \frac{1}{2} \tan^{-1} x + A$ where A is an arbitrary constant, then the value of $a$ is

\(\int_0^2 \frac{3x+1}{x^2+4} dx\)

The integral $ \int e^x \left( \frac{x + 5}{(x + 6)^2} \right) dx $ is:

The integral $ \int e^x \left( \frac{x + 5}{(x + 6)^2} \right) dx $ is:

If $\int \frac{\sin x}{\sin (x-\alpha)} dx = Ax + B \log |\sin (x-\alpha)| + c$, then the value of A and B are respectively (where c is a constant of integration)

If $\int \frac{\cos x - \sin x}{8 - \sin 2x} \, dx = \frac{1}{p} \log \left[ \frac{3 + \sin x + \cos x}{3 - \sin x - \cos x} \right] + c$, then $p = $

$\int \cos^3 x \cdot e^{\log(\sin x)} , dx = $

If $\int \frac{x^3}{\sqrt{1+x^2}} dx = a(1+x^2)^{\frac{3}{2}} + b\sqrt{1+x^2} + c$, then $a+b =$, (where $c$ is constant of integration)

$\int[1+2 \tan x(\tan x+\sec x)]^{\frac{1}{2}} d x=$

If \[ \int \frac{5 \tan x}{\tan x - 2} dx = x + a \log | \sin x - 2 \cos x | + c \], then \( a = \) (Where \( c \) is constant of integration)

Evaluate the indefinite integral:
$$\int \frac{1}{x^{\frac{1}{2}} + x^{\frac{1}{3}}}\ dx$$

$\int \operatorname{cosec}(x-a) \operatorname{cosec} x dx = $

$\int \sec^4 x \cdot \tan^4 x dx = \frac{\tan^m x}{m} + \frac{\tan^n x}{n} + c$ (where $c$ is constant of integration), then $m + n =$

$\int \frac{x+\sin x}{1+\cos x} d x=$

$\int \tan^{-1}(\sec x + \tan x) dx =$

$\int e^{\tan x}(\sec ^2 x+\sec ^3 x \sin x) d x=$

If $\int \frac{x^3}{\sqrt{1+x^2}} dx = a(1+x^2)^{\frac{3}{2}} + b\sqrt{1+x^2} + c$, then $a+b =$, (where $c$ is constant of integration)

$\int[1+2 \tan x(\tan x+\sec x)]^{\frac{1}{2}} d x=$