Bài 1: Giai Cac Phuong Trình Sau: A 7x-8=4x+7 B - Gauthmath

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Math Resources/Calculus/

Question

∈t fracx^3sqrt(x^(4-1))dxSHOW LESS0

Solution

user avatar imageAnswer\frac{1}{2}\sqrt{x^{4}+1}+CExplanationExplanation: Step 1: Substitute t = \sqrt{x^{4}+1}, which implies dt = \frac{4x^{3}}{2\sqrt{x^{4}+1}}dx. Step 2: Rewrite the integral in terms of t, which gives \int \frac{x^{3}}{\sqrt{x^{4}+1}}dx = \int \frac{1}{2}dt. Step 3: Integrate with respect to t, which is \frac{1}{2}t + C. Step 4: Substitute back for t to get \frac{1}{2}\sqrt{x^{4}+1} + C.Click to rate:17.1(111 votes)Search questionBy textBy image/screenshotDrop your file here orClick Hereto upload

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