What is the integral of sinh(x)cosh^4(x) ?

The integral of sinh(x)cosh^4(x) is (cosh^5(x))/5+C

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integral of sinh(x)cosh^4(x)

\int sinh (x) cosh^{4} (x) d x

\frac{cosh ^{5} ( x )}{5} + C

Solution steps

\int sinh (x) cosh^{4} (x) d x

Apply u-substitution

: \int u^{4} d u

= \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= \frac{u ^{5}}{5}

Substitute back

u = cosh (x)

= \frac{cosh ^{5} ( x )}{5}

Add a constant to the solution

= \frac{cosh ^{5} ( x )}{5} + C

y = 2 x^{2}, y = 3 - x

x \to 5 lim (\frac{4 x}{x - 5})

y^{^{'}} = (t + y)^{2} - 1, y (3) = 6

\int \frac{( x ^{2} + 3 x - 4 )}{x ^{3} - 4 x ^{2} + 4 x} d x

What is the integral of sinh(x)cosh^4(x) ?
The integral of sinh(x)cosh^4(x) is (cosh^5(x))/5+C