Integration by parts: ºx____dx | AP Calculus BC | Khan Academy

Worked example of finding an indefinite integral where integration by parts is applied twice. Created by Sal Khan.

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

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[Jamestheseira]

Can you narrate my life, what a voice.

[khanacademy]

will be on khan academy by the end of day.

[rwayne]

Very good Sal! Integration by parts is something that a lot of people have problems with. I think it's because textbooks tend to use u and v, which throws folks off track for some reason.

[LuanCristianThums]

When adding the constant to the function he is just trying to approach every possible antiderivative. The actual result may be "plus 128378713" or "plus -69" or it may doesn't even exist at all: that's because we are talking about derivatives, about slopes, and the slope of a constant is just 0 so it doesn't really matter on the result, it's just so that you can read the expression and add any constant or know that one may exist (or not), but remember: it doesn't matter.

[thelongbow]

he taught me more in one playlist than my entire high school integration course

[mr.robot.]

Great video, thank you very much Sal!

[Ryan-wxof]

Ive been watching these things for over a year now man i just wanted to thank you, i cant learn hardly anything from lectures but thanks to you and wolframalpha ive gone from 8th grade developmental math to calc 2 in under a year

[kishwarbhuiyan]

This video has helped me a lot to grasp this difficult idea of integration by parts. Thank you, Sal.

[EduardoRohdeEras]

thank you very much! Your classes are helping me to remember calculus!

[matthewjohnscerri]

wow i never found the integration by parts so easy!! btw what software are you using?

[ucasvb]

Make a video of the table method too, when you have some larger integration by parts chains!

[dalenassar]

Sal, You really should write the final answer as: exp(x) [x^2 -2x +2] + C. It makes the quadratic equation in x obvious.

[bigfan]

Just to let you know that I added the khan academy app to chrome and the logo is in black and white instead of the regular one. Thanks for what you do.

[yosoet]

The anti-derivative of e^{x^2} is not an "elementary" function. it can be though represented with error function

[squirt]

there is a much easier way of doing this... search up the tabular method (it is integration by parts but a faster way in situations like this where if you keeping taking the derivative of f(x) it eventually reaches 0)

[daveyboy]

agree with more samples of table method - I've also noticed that there have been a lot of new integration examples lately but they aren't on the khan academy website. (at least from what I can see). Are these types of examples exclusive to the youtube page or just delayed in being added to the website?

[_FabioSilveira]

With Khan Academy and Wolfram Alpha, who needs anything else?

[Bloodre]

Can you do the integration of (x^2)(e^(x^2)) please?

[JosCleland]

Why is +C only added right at the very end? it's probably obvious but yeah..

[shrishpandey]

the video is super but its not perfectly visible