What is the integral of cosh^2(x-1)sinh(x-1) ?

The integral of cosh^2(x-1)sinh(x-1) is (cosh^3(x-1))/3+C

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integral of cosh^2(x-1)sinh(x-1)

\int cosh^{2} (x - 1) sinh (x - 1) d x

\frac{cosh ^{3} ( x - 1 )}{3} + C

Solution steps

\int cosh^{2} (x - 1) sinh (x - 1) d x

Apply u-substitution

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

Apply u-substitution

= \int v^{2} d v

Apply the Power Rule

= \frac{v ^{3}}{3}

Substitute back

= \frac{cosh ^{3} ( x - 1 )}{3}

Add a constant to the solution

= \frac{cosh ^{3} ( x - 1 )}{3} + C

What is the integral of cosh^2(x-1)sinh(x-1) ?
The integral of cosh^2(x-1)sinh(x-1) is (cosh^3(x-1))/3+C