What is the integral from 0 to infinity of e^xsin(x) ?

The integral from 0 to infinity of e^xsin(x) is diverges

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integral from 0 to infinity of e^xsin(x)

\int_{0}^{\infty} e^{x} sin (x) d x

diverges

Solution steps

\int_{0}^{\infty} e^{x} sin (x) d x

Compute the indefinite integral:

\int e^{x} sin (x) d x = - \frac{e ^{x} cos ( x )}{2} + \frac{e ^{x} sin ( x )}{2} + C

Compute the boundaries:

\int_{0}^{\infty} e^{x} sin (x) d x =

diverges

= diverges

\int_{0}^{4} 4 x^{3} d x

\int_{0}^{\frac{π}{4}} cos^{3} (2 x) d x

\int_{a}^{b} \frac{x}{b - a} d x

\int_{- \frac{π}{2}}^{\frac{π}{2}} sin^{3} (x) d x

\int_{0}^{2 s i n (θ)} r^{2} sin (θ) d θ

What is the integral from 0 to infinity of e^xsin(x) ?
The integral from 0 to infinity of e^xsin(x) is diverges