Problem

Use substitution to find each indefinite integral…

03:19

Problem 11 Easy Difficulty

Use substitution to find each indefinite integral.
$$\int 4 x^{3} e^{2 x^{4}} d x$$

Answer

$\frac{e^{2 x^{3}}}{2}+C$

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus with Applications

Chapter 7

Integration

Section 2

Substitution

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Video Transcript

so for problem 11. We are asked to use substitution to find this indefinite integral. So for the U substitution, we're gonna let this equal, are you? And we do that because it's a function inside of a function. This function is inside that e function. So we're gonna let you equal to X to be the fourth power. So we go ahead and take the derivative of both sides. We get to you equals two times for ext three d x. So to make this easier, we could do do you over to divide both sides of the incursion by two. He goes for X cube, deed X. Now we go ahead and we'll get in like us. So the four first weaken do this part and it would be four x cubed de ETS. But we have ah 1/2. So we remove that outside the integral and all of that equals you. And then for the you part, you would do e to the you power because that is what we chose there you to be This equals won her time's a So the integral of this e to the youth is even to you and then you have to do the plus c. We'll be eating you over to you plus C and you can't leave it in terms of you. You have to plug in two X to the fourth in replacement of every U to exit before two times two weeks before we'll see. And if you simplify this, you get to e to it to the fourth over for it's to the fourth. What? See? And this would be your answer.

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