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

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

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integral of x^3cosh(x)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\int \frac{3 x ^{3} - 8 x ^{2} + 10}{x ( x - 1 ) ^{3}} d x

(y^{2} - x y) d x - x^{2} d y = 0

\frac{d}{d x} (a t)

y^{^{'''}} + 14 y^{^{''}} + 49 y^{^{'}} = 0

\int 19 ln (3 x) d x

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