Integral Calculus

$\underset{0}{\overset{1}{\int }}\sqrt{\frac{1-x}{1+x}}dx$

$\int \frac{\left(x+2\right)dx}{\sqrt{\left(x-2\right)\left(x-3\right)}}$ is equal to:

The value of $\int \cos 2x\cos 4xdx$ is

The value(s) of  ${\displaystyle \underset{0}{\overset{1}{\int }}\frac{x^4{(\mathrm{}\mathrm{}\mathrm{}1-x)}^4}{1+x^2}}dx$  is/are:

The value of the integral $\underset{0}{\overset{1}{\int }}\sqrt{\frac{\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}1-x}{1+x}}dx$ is

If $f\left(x\right)=Asin\left(\frac{\pi x}{2}\right)+B, f\text{'}\left(\frac{1}{2}\right)=\sqrt{2} \mathrm{and}\underset{0}{\overset{1}{\int }}f\left(x\right)dx=\frac{2A}{\pi },$ then constants $A$ and $B$ are respectively 

$f\left(x\right)=A\sin \left(\frac{\pi x}{2}\right)+B, f^{\text{'}}\left(\frac{1}{2}\right)=\sqrt{2}$and${\int }_0^{1}f\left(x\right)dx=\frac{2A}{\mathrm{\pi }}$, then constants $A$ and $B$ are

The value of $\underset{0}{\overset{\pi /4}{\int }}\frac{\sin x+\cos x}{9+16\sin 2x}dx$ is

If $f^{\text{'}}\left(x\right)=k(\cos x-\sin x)$, $f^{\text{'}}\left(0\right)=3, f\left(\frac{\pi }{2}\right)=15,$ find $f\left(x\right)$.

Evaluate the following :

$\int {\tan }^2\mathrm{x} \mathrm{dx}$

Evaluate $\int \frac{dx}{\sqrt{1+x}-\sqrt{x}}$

$\int \frac{(x+3)}{(x+4{)}^2}.e^{\mathit{x}}\mathit{ }dx$ is equal to 

The value of $\int \frac{1+{\cos }^{2}x}{1-\cos 2x}dx$ is

If ${\int }_0^{k}4x^3 dx=16,$ then the value of $k$ is

Let $S$ be the set of real numbers $p$ such that there is no non-zero continuous function $f:R\to R$ satisfying ${\int }_0^{x}f\left(t\right)dt=pf\left(x\right)$ for all $x\in R$. Then, $S$ is

Let $\ln x$ denote the logarithm of $x$ with respect to the base $e$ Let $S\subset R$ be the set of all points where the function $\ln \left(x^2-1\right)$ is well-defined. Then, the number of functions $f:S\to R$ that are differentiable, satisfy $f^{\text{'}}\left(x\right)=\ln \left(x^2-1\right)$ for all $x\in S$ and $f\left(2\right)=0,$ is

Evaluate the following functions w.r.t.$x$

$\int {\left(3x^2-5\right)}^{2}dx$

Find $\int \left(2x^2+e^x\right)dx$

Evaluate $\int \frac{1}{1+\sin x} \mathrm{d}x$.