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

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

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integral of (5sinh(x)+x^5)

\int (5 sinh (x) + x^{5}) d x

5 cosh (x) + \frac{x ^{6}}{6} + C

Solution steps

\int 5 sinh (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 5 sinh (x) d x + \int x^{5} d x

\int 5 sinh (x) d x = 5 cosh (x)

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

= 5 cosh (x) + \frac{x ^{6}}{6}

Add a constant to the solution

= 5 cosh (x) + \frac{x ^{6}}{6} + C

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