List of top Mathematics Questions on integral

\[ \int \frac{dx}{\sqrt{x+1}+\sqrt{x}}= \]

The integral of \(f(x)=1+x^2+x^4\) with respect to \(x^2\) is

\[ \int \frac{dx}{\sqrt{16-25x^2}}= \]

\[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{6}} \frac{\sin^5x\cos^3x}{x^4}\,dx= \]

\[ \int_0^1 x\sqrt{x^2+4}\,dx= \]

If \[ \int \frac{\sin^3x+\cos^3x}{\sin^2x\cos^2x}\,dx = A\sec x+B\cosec x+c, \] then \((A,B)\) are

\[ \int \frac{dx}{\sin^2x\cos^2x}= \]

The value of the integral \( \int_{-2\pi}^{2\pi} \sin^4 x \cos^6 x \, dx \) is equal to:

The value of the integral \( \int_{0}^{\pi/2} \sin^6 x \cos^4 x \, dx \) is equal to:

The value of the integral \( \int_{0}^{32\pi} \sqrt{1 - \cos 4x} \, dx \) is equal to:

The value of the integral \[ \int_{-\frac{\pi}{8092}}^{\frac{\pi}{8092}} \frac{\sec(2023x)}{1 + (2023)^{2023x}} \, dx \] is equal to:

The value of the integral \( \int_{-\frac{\pi}{15}}^{\frac{\pi}{15}} \frac{\cos 5x}{1 + e^{5x}} \, dx \) is equal to:

The integral \[ \int \frac{1}{\sqrt[4]{(x-1)^3(x+2)^5}} \, dx \] is equal to:

The integral $\int \frac{dx}{x(x^4 + 1)} =$

The integral $\int \frac{e^x (1 + x)}{\cos^2(x e^x)} \, dx =$

The integral $\int \frac{1}{\cos^2 x (1 - \tan x)^2} \, dx =$

If \[ f(x)=\int \frac{x^2}{(1-x^2)(1+\sqrt{1-x^2})}\,dx \] and \( f(0)=2 \), then \( f\left(\frac12\right) \) is:

The value of \[ \int \frac{x^2-1}{(x^4+3x^2+1)\tan^{-1}\left(x+\frac1x\right)}\,dx \] is:

Evaluate: \[ \int \frac{x+1}{x(1+xe^x)^2}\,dx \]

\[ \int \frac{1}{x^{1/2}+x^{1/3}}\,dx \] is equal to:

The value of \[ \int \frac{x^2-1}{x^3\sqrt{2x^4-2x^2+1}}\,dx \] is:

Evaluate the indefinite integral: \[ \int e^x (\sin x + \cos x)\, dx \]

If \(\int x^3 e^x \, dx = e^x(px^3 + qx^2 + rx + s) + C\), then find the value of \(p + q + r + s\).

The value of $\int \frac{x^2-1}{(x^4+3x^2+1)\tan^{-1}(x+\frac{1}{x})} dx$ is: