Integration Using Trigonometric Identities

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

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

${\displaystyle \int \frac{{(\cos 2x)}^{\frac{1}{2}}}{\sin x}dx}$ is equal to

$\int \frac{dx}{\sin \left(x-a\right)\sin (x-b)}$ is equal to

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

$\int \frac{dx}{\cos x+\sqrt{3}\sin x}$  is equal to

If $\int \frac{\cos 4x+1}{\cot x-\tan x}dx=k\cos 4x+c$$,$ then value $k$ is equal to

$\int \frac{\text{sin 2x}}{\text{sin 5x sin 3x}}\text{dx }$is equal to

$\int 4\sin x \mathrm{co}s\frac{x}{2}\cos \frac{3x}{2}dx$ is equal to

The value of $\sqrt{2}\int \frac{\sin \mathrm{ }x dx}{\sin \left(x-\frac{\pi }{4}\right)}$ is equal to

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 

Integrate the following w.r.t $x$:

$\frac{1}{2+\cos x-\sin x}$

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

Integrate the following function with respect to $x$
$\sin 3x\sin 2x$

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 following:

$\int \frac{1}{3+2\sin 2x+4\cos 2x}dx$