What is the integral of (6sinh(x)+x^4) ?

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

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integral of (6sinh(x)+x^4)

\int (6 sinh (x) + x^{4}) d x

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

Solution steps

\int 6 sinh (x) + x^{4} 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^{4} d x

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

\int x^{4} d x = \frac{x ^{5}}{5}

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

Add a constant to the solution

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

\int \frac{1}{x ^{2 + 1}} d x

\int 4 - (x - 1)^{2} d x

\int \frac{3 x - 2}{x ^{2} + 1} d x

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