integrate cos(logx)

integrate cos(logx)

1 Answers

Try intefration by parts:

take 1 as first function and cos(lnx) as second

I=cos(ln(x))*x-âˆ«-sin(ln(x))*x dx

I₁=âˆ«sin(ln(x))*x dx
Apply parts to it also

Then I=cos(ln(x))*x+I₁

I=cos(ln(x))*x+x*sin(ln(x))-âˆ«cos(ln(x))dx

I=cos(ln(x))*x+x*sin(ln(x))-I
2I=(cos(ln(x))+sin(ln(x)))*x

I=x*(cos(lnx)+sin(lnx))/2

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