What is the integral of (sinh(x)+sinh^3(x)) ?

The integral of (sinh(x)+sinh^3(x)) is (cosh^3(x))/3+C

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integral of (sinh(x)+sinh^3(x))

\int (sinh (x) + sinh^{3} (x)) d x

\frac{cosh ^{3} ( x )}{3} + C

Solution steps

\int sinh (x) + sinh^{3} (x) d x

Simplify

sinh (x) + sinh^{3} (x) : cosh^{2} (x) sinh (x)

= \int cosh^{2} (x) sinh (x) d x

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{u ^{3}}{3}

Substitute back

u = cosh (x)

= \frac{cosh ^{3} ( x )}{3}

Add a constant to the solution

= \frac{cosh ^{3} ( x )}{3} + C

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What is the integral of (sinh(x)+sinh^3(x)) ?
The integral of (sinh(x)+sinh^3(x)) is (cosh^3(x))/3+C