What is the integral of (6sinh(x)+x^5) ?

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

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integral of (6sinh(x)+x^5)

\int (6 sinh (x) + x^{5}) d x

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

Solution steps

\int 6 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 6 sinh (x) d x + \int x^{5} d x

\int 6 sinh (x) d x = 6 cosh (x)

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

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

Add a constant to the solution

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

\int 6 x^{2} \cdot arccos (x) d x

\int \frac{4 x - 6}{x ^{2} - 3 x + 7} d x

\int \frac{x ^{2} + 1}{x ^{4} + 10 x ^{3} + 21 x ^{2}} d x

\int x (x + 7)^{5} d x

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