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Expand the integral $\int_{0}^{2}\left(\sqrt{2x^2+1}-x\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately
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$\int_{0}^{2}\sqrt{2x^2+1}dx+\int_{0}^{2}-xdx$
Learn how to solve definite integrals problems step by step online. Integrate the function (2x^2+1)^1/2-x from 0 to 2. Expand the integral \int_{0}^{2}\left(\sqrt{2x^2+1}-x\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. First, factor the terms inside the radical by 2 for an easier handling. Taking the constant out of the radical. We can solve the integral \int\sqrt{2}\sqrt{x^2+\frac{1}{2}}dx by applying integration method of trigonometric substitution using the substitution.