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

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

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integral of x^3sinh(x)

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

x^{3} cosh (x) - 3 (x^{2} sinh (x) - 2 (x cosh (x) - sinh (x))) + C

Solution steps

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

Apply Integration By Parts

: x^{3} cosh (x) - \int 3 x^{2} cosh (x) d x

= x^{3} cosh (x) - \int 3 x^{2} cosh (x) d x

\int 3 x^{2} cosh (x) d x = 3 (x^{2} sinh (x) - 2 (x cosh (x) - sinh (x)))

= x^{3} cosh (x) - 3 (x^{2} sinh (x) - 2 (x cosh (x) - sinh (x)))

Add a constant to the solution

= x^{3} cosh (x) - 3 (x^{2} sinh (x) - 2 (x cosh (x) - sinh (x))) + C

x \to 6 + lim (7 - x)

\int \frac{( x + 4 )}{x} d x

n = 1 \sum \infty n + 1

\int \frac{3}{65} x^{2} d x

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