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The Integral of sinx -x cosx/x(x+sinx) is

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Solution: Given ,

$\ Rightarrow I=int sinx-xcosx/x(x+sinx)hspace0.1cmdx$

write , $N^r=(sinx-x)-x(1+cosx)$

$\ herefore$ $\ I=int (1/x)dx-int (1+cosx/x+sinx)dx$

$\Rightarrow I=ln x-ln (x+sinx)+c\ \Rightarrow I=ln (x/x+sinx)+c$

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Deependra Verma

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