Integral of e^(pi*x)

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Integral of e^(pi*x)

The Math Sorcerer 03.06.2026 1 152 просмотров 89 лайков

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We do a simple integral using substitution. I hope this helps someone learning Calculus. Math Courses https://freemathvids.com/ Books https://www.amazon.com/stores/The-Math-Sorcerer/author/B0DRSVPVMW/ Life Changing Books(affiliate links) Real Superpowers That Will Change Your Life: https://amzn.to/40cTxas Unstoppable Execution: Take Control, Crush Obstacles, and Win: https://amzn.to/3EqTVK3 Philosophy for Winners: Strength, Strategy, and Execution https://amzn.to/3EvSkTc Math Books(affiliate links) Superpowered Calculus: Limits, Derivatives, and Integrals: https://amzn.to/4hmqerE Calculus Alpha: Limits for Math Super Nerds: https://amzn.to/403WCrU Calculus Beta: Derivatives for Math Super Nerds: https://amzn.to/3El7NVQ Precalculus for Legends: https://amzn.to/4gk9GPT Superpowered College Algebra 1: https://amzn.to/3BMHxmx Superpowered College Algebra 2: https://amzn.to/3W40oAB Math Study Strategies: https://amzn.to/3DEMnTZ Mathematics Unlimited: https://amzn.to/40HLaT8 Core Math Skills: https://amzn.to/4hkKTMq A Book of Fractions https://amzn.to/3FOVaTI Mathematical Proofs for Beginners https://amzn.to/4k8ZNqB Courses and Other Things My Courses: https://www.freemathvids.com/ Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear https://amzn.to/3BFvcxp These are my affiliate links. As an Amazon Associate I earn from qualifying purchases. If you enjoyed this video please consider liking, sharing, and subscribing. Udemy Courses Via My Website: https://mathsorcerer.com My FaceBook Page: https://www.facebook.com/themathsorcerer My Instagram: https://www.instagram.com/therealmathsorcerer/ My TikTok: https://www.tiktok.com/@therealmathsorcerer There are several ways that you can help support my channel:) Consider becoming a member of the channel: https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join My GoFundMe Page: https://www.gofundme.com/f/support-math-education-for-the-world My Patreon Page: https://www.patreon.com/themathsorcerer Donate via PayPal: https://paypal.com/donate/?cmd=_s-xclick&hosted_button_id=7XNKUGJUENSYU ************Udemy Courses(Please Use These Links If You Sign Up!)************* Abstract Algebra Course https://www.udemy.com/course/abstract-algebra-group-theory-with-the-math-sorcerer/?referralCode=B04607DA7A7D0E29272A Advanced Calculus Course https://www.udemy.com/course/advanced-calculusreal-analysis-with-the-math-sorcerer/?referralCode=0ABDD66D061D976EE232 Calculus 1 Course https://www.udemy.com/course/calculus-1-with-the-math-sorcerer/?referralCode=E853B70ED36571CA9768 Calculus 2 Course https://www.udemy.com/course/calculus-2-with-the-math-sorcerer/?referralCode=BAA5520B32FEA9827D54 Calculus 3 Course https://www.udemy.com/course/calculus-3-with-the-math-sorcerer/?referralCode=296462D1897904C4BEB3 Calculus 1 Lectures with Assignments and a Final Exam https://www.udemy.com/course/calculus-1-lectures-with-the-math-sorcerer/?referralCode=5D425153B63A8F506E30 Calculus Integration Insanity https://www.udemy.com/course/calculus-integration-insanity-with-the-math-sorcerer/?referralCode=D533EEE31F90EDDAFF93 Differential Equations Course https://www.udemy.com/course/differential-equations-with-the-math-sorcerer/?referralCode=4F0D91B41F7DACF4EC28 Differential Equations Lectures Course (Includes Assignments + Final Exam) https://www.udemy.com/course/differential-equations-lectures-with-the-math-sorcerer/?referralCode=89E6CCC307A7A8627CD6 College Algebra Course https://www.udemy.com/course/college-algebra-with-the-math-sorcerer/?referralCode=B2929EE97EF68DB9B69F How to Write Proofs with Sets Course https://www.udemy.com/course/how-to-write-proofs-in-set-theory-with-the-math-sorcerer/?referralCode=D503A7E3FB6916CF2D27 How to Write Proofs with Functions Course https://www.udemy.com/course/how-to-write-proofs-with-functions-with-the-math-sorcerer/?referralCode=DBACD59AB7B16D4707CD Trigonometry 1 Course https://www.udemy.com/course/trigonometry-1-with-the-math-sorcerer/?referralCode=79E02DDFD4106A909AF5 Trigonometry 2 Course https://www.udemy.com/course/trigonometry-2-with-the-math-sorcerer/?referralCode=7966E40F319B4FEF6535 Statistics with StatCrunch Course https://www.udemy.com/course/statistics-with-statcrunch-by-the-math-sorcerer/?referralCode=69B27AF43D10924FF63B Thank you:)

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Integrate e^(pi*x)

Integrate e to the pi x. So, if it was just e to the x, we would get e to the x because we all know that the integral of e to the x is e to the x plus a constant. So, we have to deal with the pi. To do that, we simply let u be equal to pi x. And then we differentiate both sides here. So, du is equal to pi dx. And now we don't have a pi here in the integrand. So, we have to eliminate it here because this has to look like this. That's the goal. Whenever you get to this step, you want to make this piece here look like what's up here. So, we'll divide both sides by pi. So, we get 1 over pi du is equal to dx. All right, now we're good to go. This is equal to Well, dx is simply 1 over pi du. This is And we have e to the Well, what's pi x? That's u. And now we're in a good place. Now we can integrate. We know that the integral of e to the u is e to the u. So, this is 1 over pi e to the u plus our constant. But, we are not done, right? Because u is equal to pi x. This is 1 over pi e to the pi x plus our constant of integration. And that's it, my friends. If you enjoyed this content, check out my books and courses. Links in the description. Subscribe, like, share, all that good stuff you're supposed to do. Stay strong.

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