Integration Using Trigonometric Identities

Evaluate :${\displaystyle {\int }_{\frac{\pi }{6}}^{\frac{\pi }{3}}\frac{dx}{1+\sqrt{\cot x}}}$

Evaluate ${\displaystyle {\int }_0^{\pi }\frac{x\sin x}{1+{\cos }^{2}x}dx}$

Find ${\displaystyle \int \frac{2x}{(x^2+1)(x^4+4)}}$dx

Evaluate the following:

${\displaystyle \int \frac{(1+\cos x)}{x+\sin x}\text{d}x}$

Find the integrals of the function:

sin³ x cos³ x

Integrate the function ${\displaystyle \frac{\cos \left(\text{x + a}\right)}{\sin \left(\text{x + b}\right)}}$ w.r.t. x.

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

Find the integrals of the function:

sin x sin 2x sin 3x