What is the integral of 2x^4+5e^x-sin(x) ?

The integral of 2x^4+5e^x-sin(x) is (2x^5)/5+5e^x+cos(x)+C

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integral of 2x^4+5e^x-sin(x)

\int 2 x^{4} + 5 e^{x} - sin (x) d x

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

Solution steps

\int 2 x^{4} + 5 e^{x} - sin (x) 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 x^{4} d x + \int 5 e^{x} d x - \int sin (x) d x

\int 2 x^{4} d x = \frac{2 x ^{5}}{5}

\int 5 e^{x} d x = 5 e^{x}

\int sin (x) d x = - cos (x)

= \frac{2 x ^{5}}{5} + 5 e^{x} - (- cos (x))

Simplify

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

Add a constant to the solution

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

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What is the integral of 2x^4+5e^x-sin(x) ?
The integral of 2x^4+5e^x-sin(x) is (2x^5)/5+5e^x+cos(x)+C