Integral of xtan^-1(x), step by step, using integration by parts. скачать в хорошем качестве

Integral of xtan^-1(x), step by step, using integration by parts.

🎓 Welcome to the Math Magic Show! 🎩✨ In this video, we'll find the antiderivative of xtan^-1(x) using integration by parts! 📚🔍 In order to integrate xtan^-1(x) step by step, we'll use integration by parts, with the acronym ILATE to help us choose the right functions for u and dv. 🧠💡 🔹 u = tan^-1(x) (Inverse trig function) 🔹 dv = x dx Now, let's find du and v 🔹 du = (1 / (1 + x²)) dx 🔹 v = (1/2) x² Integration by parts formula u dv = u v - ∫v du 🧩 Applying the formula, we get (1/2) x² tan^-1(x) - ∫(1/2) x² (1 / (1 + x²)) dx Using polynomial long division, we rewrite the integrand as (1/2) x² tan^-1(x) - (1/2) ∫(1 - (1 / (x² + 1))) dx Now, you can easily integrate the function and find the antiderivative! 🎉🏁 Enjoy learning math with our Math Magic Show! Don't forget to like, share, and subscribe for more amazing math content! 😊✌️ 👕 Buy a clever and unique math t-shirt: https://rb.gy/rmynnq 🔍 Find the power series representation of 1/(x+5) and the interval of convergence. 📚 Resources: http://calculuscoaches.com/index.php/... 🛍️ Please visit our Merch Stores and help support the spreading of knowledge:) Our T-Shirt Merch: https://my-store-cf0bfb.creator-sprin... Our Amazon Store for Awesome Merch too: https://amzn.to/3OttJgU 🎵 Amazon Music Free Trial: https://amzn.to/3PzvbzY 🎁 Amazon Prime Free Trial: https://amzn.to/3PUrmoN 📚 Audible Plus Free Trial: https://amzn.to/3RPcrxI 📖 Kindle Unlimited Free Trial: https://amzn.to/3yXGZVs 🎮 Video Game Bestsellers: https://amzn.to/3aZSX9h 💖 Are you a fan of our content and want to support us in a tangible way? Why not check out our merchandise? We have a wide range of products, including t-shirts, hoodies, phone cases, stickers, and more, all featuring designs inspired by our brand and message. By purchasing our merchandise, not only will you be showing your support for our work, but you’ll also be able to enjoy high-quality, stylish products that you can wear or use in your daily life. And best of all, a portion of the proceeds goes directly towards helping us continue to create and produce the content you love. So what are you waiting for? Head over to our online store now and browse our selection of merchandise. We’re sure you’ll find something you love.💖