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$\int_{0}^{1}\frac{x^{3}}{\sqrt{8-8x}}dx$
Learn how to solve problems step by step online. Integrate the function ((x^6)/(4-8x+4))^1/2 from 0 to 1. Simplify the expression inside the integral. Rewrite the fraction \frac{x^{3}}{\sqrt{8-8x}} inside the integral as the product of two functions: x^{3}\frac{1}{\sqrt{8-8x}}. We can solve the integral \int x^{3}\frac{1}{\sqrt{8-8x}}dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du.