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Expand the fraction $\frac{x-\arctan\left(2x\right)}{1+4x^2}$ into $2$ simpler fractions with common denominator $1+4x^2$
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$\int\left(\frac{x}{1+4x^2}+\frac{-\arctan\left(2x\right)}{1+4x^2}\right)dx$
Learn how to solve integral calculus problems step by step online. Find the integral int((x-arctan(2x))/(1+4x^2))dx. Expand the fraction \frac{x-\arctan\left(2x\right)}{1+4x^2} into 2 simpler fractions with common denominator 1+4x^2. Simplify the expression inside the integral. Rewrite the fraction \frac{x}{1+4x^2} inside the integral as the product of two functions: x\frac{1}{1+4x^2}. We can solve the integral \int x\frac{1}{1+4x^2}dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula.