Question

Find the integrals of the function: $\frac{sin^2\ x}{1+ cos\ x}$

Answer 1

Answer:

Step-by-step explanation:

Concept:

$a^2-b^2=(a-b)(a+b)$

The given integral is solved by decomposition method.

In decomposition method, the given integrand(non-integrable function) is decomposed into integrable functions by using algebraic identities, trigonometry identities.

$\int{\frac{sin^2x}{1+cosx}}\:dx\\\\=\int{\frac{1-cos^2x}{1+cosx}}\:dx\\\\=\int{\frac{1^2-cos^2x}{1+cosx}}\:dx\\\\=\int{\frac{(1-cosx)(1+cosx)}{1+cosx}}\:dx\\\\=\int{(1-cosx)}\:dx\\\\=\int{1}\:dx-\int{cosx}\:dx$

= x - sinx + c