What is the integral of cos t/t where limits are 1 to x ? My book says that it is sinx/x - sin1 + integral (from 1 to x) sin t/ t^{2 }dt for all x>=1. I can't figure out how . Please help.
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Originally Posted by mrmaaza123 What is the integral of cos t/t where limits are 1 to x ? My book says that it is sinx/x - sin1 + integral (from 1 to x) sin t/ t^{2 }dt for all x>=1. I can't figure out how . Please help. Use integration by parts. $\displaystyle u=\frac{1}{t} \implies du=-\frac{1}{t^2}dt$ and $\displaystyle dv=\cos(t) \implies v=\sin(t)$ This gives $\displaystyle \int_{1}^{x} \frac{\cos(t)}{t}dt=\frac{\sin(t)}{t}\bigg|_{t=1}^ {t=x}+\int_{1}^x\frac{\sin(t)}{t^2}dt$
Oh, yes. Thank you, i don't really know how i overlooked that !
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