Integration by parts two times (KristaKingMath)

Learn how to use the integration by parts formula to find the integral of a function involving the exponential (e^x) and a trigonometric function. To complete this problem, you'll need to identify which part of the function will be set equal to u, and which part of the function will be set equal to dv. Then you'll take the derivative of u to find du and take the integral of dv to find v. Then you'll plug u, du, v and dv into your integration by parts formula. With this particular problem, you'll have to perform a second round of integration by parts. After using integration by parts twice, you'll have to move the remaining integral from the right hand side to the left hand side, and then divide both sides by the coefficient from the left hand side in order to solve for the original integral.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[huhmarsook]

I used to watch your videos when I was taking AP calc in my high school days and now I came back for more advanced calc. I cannot thank you enough. Your explanations are detailed, concise, and considerate. Thank you so much for the videos.

I have been teaching for more than 38 years. You are amazingly good and efficient. Thank you. The Planetary Society Argentina.

[kristakingmath]

I'm so glad you like my teaching style! :)

[astrotaco_bps]

engineering student here... clicked subcribed so fast xD

[BboyRiiko]

thank you GOD for having someone with enthusiasm and the ability to teach/instruct WITHOUT a monotone voice. The fact that you reiterate why you do certain steps is why I can follow along :] 

[jordanhenry]

Best step by step of Integration By Parts on the internet. Thank you Krista!

[admiresithole]

You have no clue how you saved my Cal 3 grade .Thank you for your service.God Bless you in every way possible

[alok]

Thank you so much, I have differential equation exam in 12 minutes and you explained this beautifully. It's been 8 years, I hope you are in good health and doing great in life.👏👏

[mohammadzainfarooqui]

Even after completing 9 years this video remains very helpful to all those who struggle at calculus.

[kristakingmath]

for me it's mostly about gaining an intuition through a lot of practice, but the LIATE rule can also give you a decent idea. it tells you to pick a Logarithmic function, an Inverse trig function, and Algebraic function, a Trig function, or an Exponential function, in that order, if you have one of them in your integral. hope that helps! :)

[kristakingmath]

I'm glad I can at least teach on YouTube and help people all over the world that way. :)

[clt]

This BLEW MY MIND! I was like "no way is this getting simpler!" Then BAM

[magicguy]

In this problem, the choice of u and dv don't matter because neither e^(7x) or cos(2x) become appreciably simpler when integrated or differentiated (adds a constant of 7 or 1/7 in the e^(7x) and adds a -2 or a 1/2 factor and changes cos to sin in cos(2x) case)

[viovy]

Best explanation I've ever seen ! Clear and precise, btw your voice is wonderful for teaching Math : D

[caracraig-mccourt]

night before my exam and had no idea what this was called but through a lot of google searches I found this and thank goodness, you are a life saver! I owe you so much!

[skoolscribe]

One of the best IBP explanations I've come across.

[mjones]

Thank you for being old-fashioned (i.e. mathematically rigorous) enough to take that last step to factor the answer. Too many other math YouTubers would simply leave it unfactored. This in itself could mark the difference between a five versus a four on the AP exams.

[Jjacobs]

Cal 2 is so difficult. People are dropping like flies in my class. Thank GOD you are posting these videos.

[umarameen]

U r so good teacher and i wana ur type of explain everything so politely like mother deals with her
And i love ur these type of expressions...
Love u....😘

[muhammadhamzajaved]

Miss, you have helped me alot in my practice of integration, i can't thank you enough. Im having paper of Maths on 5th May .Me and my friend, we have practiced everything from limits, derivatives, Conics, analytical geometry and the mighty " integration " but yet we feel nervous and tense from keeping ourselves away from mistakes . We hope that paper will be easy, i just pray everything goes smoothly . Please Miss pray for me and my friend to get success and victory in maths