What is the integral of (2cosh(x)+x^4) ?

The integral of (2cosh(x)+x^4) is 2sinh(x)+(x^5)/5+C

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integral of (2cosh(x)+x^4)

\int (2 cosh (x) + x^{4}) d x

2 sinh (x) + \frac{x ^{5}}{5} + C

Solution steps

\int 2 cosh (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 2 cosh (x) d x + \int x^{4} d x

\int 2 cosh (x) d x = 2 sinh (x)

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

= 2 sinh (x) + \frac{x ^{5}}{5}

Add a constant to the solution

= 2 sinh (x) + \frac{x ^{5}}{5} + C

\int x tan (3 x^{2}) d x

\int \frac{1}{x ( 3 x + 1 )} d x

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

\int cosh (y) d y

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

What is the integral of (2cosh(x)+x^4) ?
The integral of (2cosh(x)+x^4) is 2sinh(x)+(x^5)/5+C