Problem

Integrate the functions. $$ x \tan ^{-1} x $$

02:30

Problem 7 Easy Difficulty

Integrate the functions.
$$
x \sin ^{-1} x
$$

Answer

Related Courses

Calculus 2 / BC

NCERT Class 12 Part 2 - Math

Chapter 7

Integrals

Section 6

Integration by Parts

Discussion

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Video Transcript

We have our number seven in this problem we have to integrate exile universe X. Using integration by parts. So we'll be using the islet rule for choosing to choose the first function. So I L A I was in verse So we'll be choosing this as first function, excess second function. So according to integration by parts we'll be writing first function first and then Integration of 2nd function minus differentiation of 1st function. Integration of second function and dx. This is signed over sex And to access choir by two minus. Okay, this is an oversexed. So one by when my experiment road and access choir by two dx. Okay, so this will be access acquired by two and was x minus access by by one of minus X squared DNC. It's not. We have to integrate it. Let us take this away and integrate and then put it back here. This is a question # one. Let us say access required by one minus X squared could build an as Access choir plus one Access quite a -1. All right, okay. Access Square -1 Plus one. Bye. one of my sex squinted route so this is minus one of my sex square by when my sex square underwrote plus one by one month. That's quite underwrote. And if we need to integrate just integrated dx dx. So this will become minus one -X. Esquire Raised the power one x 2 dx and this will be equal to just run by one minus X squared dx. Okay okay so this could be written as one minus X squared on the road dx. So we have formula for this minus integration of one minus X. Esquire underwrote. Is okay anything missing Access required by 2? Yes, it was here 2 1 x two. Okay. Mhm. So this will become 1 -1 square underwrote integration. So this is max by too billion to All right, the formula for this Okay Yes this will be minus uh one bite acts by two X by two after that one minus X squared less cleaning one x 2 sign was x by a okay no problem that's all it is right like plus one by two sign in verse excellent visit for it's only less. This will be signing square sign verse X One man's X Square signed for six Okay so that is plug in here will be getting access choir by two from one Access choir by two signing over sex sign over sex this M -1 x two. So it will become bless acts by four one minus X squared Bless one x 4 sign was explicit saM was X plus C. So access choir by two I'm over six place X by 41 minus X squared Plus five x 4 signing was explicitly so they should be the answer thank you.

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