Question

Exercise is mixed —some require integration by parts, while others can be integrated by using techniques discussed in the chapter on Integration.
∫x^3ex^4 dx.

Answer 1

Answer:

$\frac{ex^{8}}{8}+C$

Step-by-step explanation:

We have been given an indefinite integral $\int \:x^3ex^4\:dx$. We are asked to integrate it.

First of all, we will factor out the constant as:

$e\int \:x^3x^4\:dx$

$e\int \:x^{3+4}\:dx$

$e\int \:x^{7}\:dx$

Using power rule, we will get:

$e*\frac{x^{7+1}}{7+1}+C$, where, C is a constant.

$e*\frac{x^{8}}{8}+C$

$\frac{ex^{8}}{8}+C$

Therefore, the value of the given integral would be $\frac{ex^{8}}{8}+C$.