Question

( I=int(log x+sin x) cos x d x )
( I=int(x+sin x) cos x d x )
( I=int x cos x d x+int sin x cos x d x )
( begin{aligned} therefore int f(x) g(x) d x=& f(x) int g(x) d x &left.+int f^{prime}(x) int g(x) d xright] d x end{aligned} )
( f(x)= ) Ist function ( g(x)=I ) function -according there ( g f(x)=x ) & ( g(x)=cos x )
( begin{aligned} text { Let } I_{1} &=int x cos x d x &left.=x int cos x d x+int frac{d}{d x}(x) int cos x d xright] d x &=x sin x+int sin x d x end{aligned} )
( I_{1}=x sin x quad a_{3}-cos x+c_{1} )
( sin _{2} pi=x sin x-cos x+c_{1}+int sin x cos x d x )
( Rightarrow I=x sin x-cos x+c_{1}+int_{12} t d t )
( I=x sin x-cos x+c_{1}+frac{t^{2}}{1-x sin x-cos x+frac{sin ^{2} x}{2}+frac{2}{c}}{y}=frac{1}{left(c=4+c_{2}right)} )

# 7. Evaluate az + sin x) co zdz

Solution