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

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

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

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

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

Solution steps

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

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

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

\int 2 e^{x} d x = 2 e^{x}

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

Simplify

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

Add a constant to the solution

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

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

- \frac{sin ^{2} ( 2 t )}{4}

\frac{d}{d x} ((arctan (8 x))^{2})

\frac{d}{d x} (ln (1 + e^{x}))

\frac{d}{d x} (4 (x^{3} - 1)^{3})

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