How do you integrate $sinh 2 x e^{cosh 2 x} d x$ $sinh2xe^(cosh2x) dx$ ?

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How do you integrate $sinh 2 x e^{cosh 2 x} d x$ $sinh2xe^(cosh2x) dx$ ?

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Answer 1 · 2015-03-04T19:14:33

The answer is: $\frac{1}{2} e^{cosh (2 x)} + c$ $1/2e^cosh(2x)+c$ .

$\int sinh 2 x e^{cosh (2 x)} d x = \frac{1}{2} \int 2 sinh 2 x e^{cosh (2 x)} d x = \frac{1}{2} e^{cosh (2 x)} + c =$ $intsinh2xe^cosh(2x)dx=1/2int2sinh2xe^cosh(2x)dx=1/2e^cosh(2x)+c=$ .

This is because:

$inte^f(x)*f'(x)dx=e^f(x)+c$ .

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How do you integrate $sinh 2 x e^{cosh 2 x} d x$ $sinh2xe^(cosh2x) dx$ ?

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