What is the integral of (x^2+2cosh(x)) ?

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

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integral of (x^2+2cosh(x))

\int (x^{2} + 2 cosh (x)) d x

\frac{x ^{3}}{3} + 2 sinh (x) + C

Solution steps

\int x^{2} + 2 cosh (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int 2 cosh (x) d x = 2 sinh (x)

= \frac{x ^{3}}{3} + 2 sinh (x)

Add a constant to the solution

= \frac{x ^{3}}{3} + 2 sinh (x) + C

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