# Thread: Integrate exp(-x) sin(tx) /x

1. ## Integrate exp(-x) sin(tx) /x

By differentiating through the integral sign, evaluate:

1) $\int_0^{\infty} (\exp(-x) \sin (tx)) / xdx$

2) $\int_0^{\infty} (x^2 + a) ^{-n} dx$ where n is a positive integer and case i) a > 1 case ii) a>0.

2. Originally Posted by Amanda1990

1) $\int_0^{\infty} (\exp(-x) \sin (tx)) / xdx$
Put $f(t)=\int_{0}^{\infty }{\frac{e^{-x}\sin (tx)}{x}\,dx},$ and differentiate.