Learn how to solve problems step by step online. Find the integral int(4x(3x^2-x^3+1))dx. The integral of a function times a constant (4) is equal to the constant times the integral of the function. Rewrite the integrand x\left(3x^2-x^3+1\right) in expanded form. Expand the integral \int\left(3x^{3}-x^{4}+x\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral 12\int x^{3}dx results in: 3x^{4}.

Find the integral int(4x(3x^2-x^3+1))dx