What is the integral of x^3ex^4+5 ?

The integral of x^3ex^4+5 is (ex^8)/8+5x+C

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integral of x^3ex^4+5

\int x^{3} e x^{4} + 5 d x

\frac{e x ^{8}}{8} + 5 x + C

Solution steps

\int x^{3} e x^{4} + 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 x^{3} e x^{4} d x + \int 5 d x

\int x^{3} e x^{4} d x = \frac{e x ^{8}}{8}

\int 5 d x = 5 x

= \frac{e x ^{8}}{8} + 5 x

Add a constant to the solution

= \frac{e x ^{8}}{8} + 5 x + C

\int \frac{sin ( 2 x )}{sin ^{2} ( x )} d x

\frac{\partial}{\partial t} (e^{π t})

n = 1 \sum \infty \frac{n + 1}{n + 2}

x \to 4 lim (\frac{x - 2}{x})

\frac{d}{d t} (s t)