Integration Using Trigonometric Identities

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

Evaluate : $\int \sqrt{\tan \theta } d\theta$ [Take $\sqrt{\tan \theta }=t$]

The value of $\int 4\sin x\cos \frac{x}{2}\cos \frac{3x}{2}dx$ is equal to

$\int {\cos }^{3}x dx$ is equal to 

If $\int \frac{2\sin x+3\cos x}{3\sin x+4\cos x}dx=A\log |3\sin x+4\cos x|+Bx+c$, then $A \mathrm{and} B$ are

Evaluate: $\int \frac{1}{1+\sin x+\cos x}dx$

If $\int \frac{1+\cos \left(4x\right)}{\cot \left(x\right)-\tan \left(x\right)}dx=k\cos \left(4x\right)+c,$ then

If $\int \frac{2\cos x+3\sin x}{3\cos x+4\sin x}dx$$=Ax+B\ln \left|3\cos x+4\sin x\right|+C$, then $\left(A+B\right)$ is equal to

Evaluate the integral$\int 4\cos \left(x+\frac{\pi }{6}\right)\cos 2x.\cos \left(\frac{5\pi }{6}+x\right)dx$ (where $c$ is constant of integration)

$\int \frac{\sqrt{\mathrm{t}\mathrm{a}\mathrm{n}x}}{\mathrm{s}\mathrm{i}\mathrm{n}x\mathrm{c}\mathrm{o}\mathrm{s}x}dx=$

Integral: $\int \frac{\mathrm{s}\mathrm{i}\mathrm{n}x-\mathrm{c}\mathrm{o}\mathrm{s}x}{\sqrt{\mathrm{s}\mathrm{i}\mathrm{n}2x}}dx$ equals: (where $c$ is constant of integration)

Consider the indefinite integral $\int \left(\frac{\cos 4x+1}{\cot x-\tan x}\right)dx=f\left(x\right)+c$ then fundamental period of $f\left(x\right)$ is: (where $c$ is constant of integration)

Indefinite integral$\int \frac{\mathrm{s}\mathrm{i}{\mathrm{n}}^{3}xdx}{\left(\mathrm{c}\mathrm{o}{\mathrm{s}}^{4}x+3\mathrm{c}\mathrm{o}{\mathrm{s}}^{2}x+1\right)\mathrm{t}\mathrm{a}{\mathrm{n}}^{-1}\left(\mathrm{s}\mathrm{e}\mathrm{c}x+\mathrm{c}\mathrm{o}\mathrm{s}x\right)}$ is equal to (where $c$ is constant of integration)

Integration of $\int \frac{\sec x}{\sec x+\tan x}dx$ equals: (where $C$ is constant of integration)

The value of$\int \frac{1}{1+\sin x}dx=$_____

$\int \frac{\cos x-\sin x}{7-9\sin 2x}dx=$

Find the value of $P$, if$\int \frac{\sqrt{\cot x}}{\sin x\cos x}\mathrm{d}\mathrm{x}=P\sqrt{\cot x}+Q$.

$\int {\sin }^{3}xdx=$

Find the ordered triplet $(A, B, \lambda )$, If $\int \frac{2\cos x-\sin x+\lambda }{\cos x+\sin x-2}dx=A{\log }_e\left(\left|\cos x+\sin x-2\right|\right)+Bx+C$.