Question

( 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} )

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

Solution