Learn how to solve problems step by step online. Find the integral int(x(5x^3+15x)^3(3x^2+3))dx. Rewrite the integrand x\left(5x^3+15x\right)^3\left(3x^2+3\right) in expanded form. Expand the integral \int\left(375x^{12}+3750x^{10}+13500x^{8}+20250x^{6}+10125x^{4}\right)dx into 5 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int375x^{12}dx results in: \frac{375}{13}x^{13}. The integral \int3750x^{10}dx results in: \frac{3750}{11}x^{11}.

Find the integral int(x(5x^3+15x)^3(3x^2+3))dx