What is the integral of e^xsinh(x) ?

The integral of e^xsinh(x) is sinh(x)e^x-1/2 (x+1/2 e^{2x})+C

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integral of e^xsinh(x)

\int e^{x} sinh (x) d x

sinh (x) e^{x} - \frac{1}{2} (x + \frac{1}{2} e^{2 x}) + C

Solution steps

\int e^{x} sinh (x) d x

Apply Integration By Parts

: sinh (x) e^{x} - \int cosh (x) e^{x} d x

= sinh (x) e^{x} - \int cosh (x) e^{x} d x

\int cosh (x) e^{x} d x = \frac{1}{2} (x + \frac{1}{2} e^{2 x})

= sinh (x) e^{x} - \frac{1}{2} (x + \frac{1}{2} e^{2 x})

Add a constant to the solution

= sinh (x) e^{x} - \frac{1}{2} (x + \frac{1}{2} e^{2 x}) + C

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\int_{3}^{\infty} \frac{1}{x ^{2} - 4} d x

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\int_{0}^{2 π} cos^{2} (x s i) n^{2} x d x

What is the integral of e^xsinh(x) ?
The integral of e^xsinh(x) is sinh(x)e^x-1/2 (x+1/2 e^{2x})+C