5

Find the indefinite integraldx Hx-6dx = Nx-6...

Question

Find the indefinite integraldx Hx-6dx = Nx-6

Find the indefinite integral dx Hx-6 dx = Nx-6



Answers

Evaluate the indefinite integral.

$ \displaystyle \int x^2 e^{x^3} \, dx $

U b l n x dvb x squared dx So do you. Is one over X dx Envy is X to the 3rd over three. So we get you ve one third execute L n x minus the integral of e d U. So one third X squared dx. So 1/3 x cubed, LNX minus one third Next to the 3/3 plus C. So one third X cubed L n x -1 9th x cubed plus CIA.

Really you is the natural oven acts, which means that de you is one over x t ax, which means that de axe is a x t you. Which means now we know we have 1/3 u Q plus seeks to use the power rule and then we backs up to you is natural look of X, which gives a solution of 1/3 time's naturally with Max cute plus secret under the U. S. Cute.

Let's start off here by just factoring the denominator. So we pull out of X and then let's do it. Use up here, you equals ln that do you is one over x gx so we can write this in a girl is one over humanise one, Do you? They do. You is equal to one over x t x. So that's taking care of this part right here, Phil. And then the U minus. Juan is taking care of the Ellen minus one. Now this we could integrate. That's just natural log. You minus one. Plus he now, if this minus one was bothering you, you can do it. A substitution here and you'LL arrive at this answer and then natural log. And finally, just come back up here and replace you with natural log of X. So we have natural lot Absolute value. Natural log X minus one closer constancy. And that's our final answer.

To evaluate a given integral, we will do integration by parts. And in here we want to let you equal to the algebraic expression X and DV will be the remaining expression erase two X. Dx. So from here we get differential of you equal to the differential effects and V will be the integral of devi that is the integral of erase xD X equal to itself erased two X. So by integration by parts, this is equal to U times V minus the integral of E times do you? That's equal to x times erase two x minus the integral V which is erased two X. And then the X. And then integrating erase X. D X. Ug gets X times erase the X minus erase two X. And then plus C. And so this is our anti derivative.


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