What is the integral of (4cosh(x)+x^3) ?

The integral of (4cosh(x)+x^3) is 4sinh(x)+(x^4)/4+C

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integral of (4cosh(x)+x^3)

\int (4 cosh (x) + x^{3}) d x

4 sinh (x) + \frac{x ^{4}}{4} + C

Solution steps

\int 4 cosh (x) + x^{3} 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 4 cosh (x) d x + \int x^{3} d x

\int 4 cosh (x) d x = 4 sinh (x)

\int x^{3} d x = \frac{x ^{4}}{4}

= 4 sinh (x) + \frac{x ^{4}}{4}

Add a constant to the solution

= 4 sinh (x) + \frac{x ^{4}}{4} + C

What is the integral of (4cosh(x)+x^3) ?
The integral of (4cosh(x)+x^3) is 4sinh(x)+(x^4)/4+C