What is the integral of (4cosh(x)+x^5) ?

The integral of (4cosh(x)+x^5) is 4sinh(x)+(x^6)/6+C

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integral of (4cosh(x)+x^5)

\int (4 cosh (x) + x^{5}) d x

4 sinh (x) + \frac{x ^{6}}{6} + C

Solution steps

\int 4 cosh (x) + x^{5} 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^{5} d x

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

\int x^{5} d x = \frac{x ^{6}}{6}

= 4 sinh (x) + \frac{x ^{6}}{6}

Add a constant to the solution

= 4 sinh (x) + \frac{x ^{6}}{6} + C

What is the integral of (4cosh(x)+x^5) ?
The integral of (4cosh(x)+x^5) is 4sinh(x)+(x^6)/6+C