What is the integral of (4sinh(x)+x^7) ?

The integral of (4sinh(x)+x^7) is 4cosh(x)+(x^8)/8+C

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integral of (4sinh(x)+x^7)

\int (4 sinh (x) + x^{7}) d x

4 cosh (x) + \frac{x ^{8}}{8} + C

Solution steps

\int 4 sinh (x) + x^{7} 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 sinh (x) d x + \int x^{7} d x

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

\int x^{7} d x = \frac{x ^{8}}{8}

= 4 cosh (x) + \frac{x ^{8}}{8}

Add a constant to the solution

= 4 cosh (x) + \frac{x ^{8}}{8} + C

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What is the integral of (4sinh(x)+x^7) ?
The integral of (4sinh(x)+x^7) is 4cosh(x)+(x^8)/8+C