What is the integral of cosh^5(x)sinh(x) ?

The integral of cosh^5(x)sinh(x) is (cosh^6(x))/6+C

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integral of cosh^5(x)sinh(x)

\int cosh^{5} (x) sinh (x) d x

\frac{cosh ^{6} ( x )}{6} + C

Solution steps

\int cosh^{5} (x) sinh (x) d x

Apply u-substitution

: \int u^{5} d u

= \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= \frac{u ^{6}}{6}

Substitute back

u = cosh (x)

= \frac{cosh ^{6} ( x )}{6}

Add a constant to the solution

= \frac{cosh ^{6} ( x )}{6} + C

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What is the integral of cosh^5(x)sinh(x) ?
The integral of cosh^5(x)sinh(x) is (cosh^6(x))/6+C