List of top Mathematics Questions on Integration asked in MHT CET

If \(u\) and \(v\) are functions of \(x\), then \(\int \frac{1}{v^3}(uv\frac{du}{dx}-u^2\frac{dv}{dx})dx =\)

Let \(f(x) = 1-\frac{1}{x},g_2(x) = f(f(x)),g_3(x) = f(f(f(x)))\) and so on. If \(\int x\cdot g_{2026}(x)\,dx = \int g_{2025}(x)\,dx+h(x)+c\), then \(h(x) =\)...

If \(f(x) = \frac{1}{logx}\) and \(g(x) = \frac{1}{(logx)^2}\), then the value of \(\int [f(x)-g(x)]\,dx\) is...

Let \(f(x) = x\), \(f_1(x) = f(logx)\), \(f_2(x) = f_1(logx)\), \(f_3(x) = f_2(logx)\), \(\ldots\) and so on. Then \(\int \frac{1}{f(x)\,f_1(x)\,f_2(x)\,\ldots f_{2026}(x)}\,dx = \ldots\)

If \(\int f^'(x)\cdot e^{x^2}\,dx = (x-1)\cdot e^{x^2}+k\), where \(k\) is constant of integration, then \(f(x) = \ldots\)

If \(f^'(x) = \frac{(\sqrt{x}+1)e^{\sqrt{x}}}{\sqrt{x}}\) and \(f(0) = e\) then \(f(1) = \ldots \ldots \ldots \ldots\)

The value of \(\int \frac{sin^3x}{(cos^4x+3cos^2x+1)tan^{-1}(secx+cosx)}\,dx\) is

If \(\int \sqrt{2}\sqrt{1+sinx}\,dx = -4cos(ax+b)+c\), then the value of \(a,b\) respectively are...

If \(\int \frac{x+1}{x^2+1}dx = tan^{-1}x+g(x)+c\), where \(c\) is constant of integration, then the function \(g(x)\) is monotonically increasing in the interval

\(\int \frac{x}{x+2}dx\) is equal to

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

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

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

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

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

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

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

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

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 $$\int \frac{dx}{\cos x \sqrt{\cos 2x}}$$