List of top Mathematics Questions on Integration asked in MHT CET

Evaluate the integral \[ \int \cos \left( \frac{\pi x}{6} \right) \cos \left( \frac{\pi x}{3} \right) \, dx. \]

Evaluate the integral: \[ \int \frac{\sin x}{5\sin^2 x + 6\cos^2 x} \, dx \]

$\int \frac{dx}{(x + a)^{9/7} (x - b)^{5/7}}$ = ______.

$\int \frac{x^4 \cos(\tan^{-1} x^5)}{1 + x^{10}} dx$ equals ______.

$\int \frac{\sqrt{\tan x}{\sin x \cdot \cos x} \, dx = $ ______.

$\int\frac{dx}{x^{\frac{1}{2}}+x^{\frac{1}{3}}}=Ax^{\frac{1}{2}}+Bx^{\frac{1}{3}}+Cx^{\frac{1}{6}}+D~log(x^{\frac{1}{6}}+1)+k$, then values of A, B, C and D are}

$\int\frac{dx}{sin^{2}x~cos^{2}x}=$

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

If the sum of the squares of the distance of the point $\text{P}(x, y, z)$ from the co-ordinate axes is 242 , then the distance of the point P from the origin is units.

The ratio of the areas bounded by the curves $y = \cos x$ and $y = \cos 2x$ between $x = 0, x = \frac{\pi}{3}$ and X -axis is

The statement pattern $[(p \rightarrow q)\land \sim q] \rightarrow r$ is a tautology when $r$ is equivalent to

Evaluate the integral with square root in denominator. \[ \int \frac{\sin 2x \cos 2x}{\sqrt{9-\cos^4 2x}}\,dx \]

Evaluate the following integrals: \[ \int \frac{(x^4 + 1)}{x(2x + 1)^2} \, dx \] and \[ \int \frac{1}{x^4 + 5x^2 + 6} \, dx \]

Evaluate the integral: $\int e^{(e^x + x)} dx$

Evaluate the indefinite integral $$\int \frac{dx}{\cos x \sqrt{\cos 2x}}$$

If $\int \frac{\sqrt{x}}{x(x+1)} \, dx = k \tan^{-1} m + c$ (where $c$ is a constant of integration), then

If $\int \frac{1+x^2}{1+x^4} d x=\frac{1}{\sqrt{2}} \tan ^{-1}\left[\frac{f(x)}{\sqrt{2}}\right]+c$, then $f(x)=$