Question

I ) 1-91-72, where vo, a and Find the integrals of the following functions: COS X (1+ sin x)? (bx" +c) axn-1

JEE/Engineering Exams

Maths

Solution

118

4.0 (1 ratings)

( int frac{cos x}{(1+sin x)^{2}} d x ) ( begin{aligned} 1+sin x &=t cos x d x &=d t end{aligned} ) ( =int_{t^{2}}^{1} d t ) ( =-1 / t^{t} ) ( =-1 / 1+sin x^{+d} ) ( theta=int frac{a x^{n-1}}{b x^{n}+c} d x ) ( b x^{n}+c=t ) ( quad b n x^{n-1} d x=d t ) ( =int frac{d t}{t} x^{n-1} d x=frac{d t}{b} ) ( =frac{a}{b n} ln t ) ( =frac{a}{b n} ln b x^{n} )