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The integral of a function times a constant ($2$) is equal to the constant times the integral of the function
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$2\int x\left(x+1\right)dx$
Learn how to solve integral calculus problems step by step online. Find the integral int(2x(x+1))dx. The integral of a function times a constant (2) is equal to the constant times the integral of the function. Rewrite the integrand x\left(x+1\right) in expanded form. Expand the integral \int\left(x^2+x\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral 2\int x^2dx results in: \frac{2}{3}x^{3}.