Exercise
$\int\:x^3\left(x^2+1\right)^8dx$
Step-by-step Solution
Learn how to solve differential calculus problems step by step online. Find the integral int(x^3(x^2+1)^8)dx. Rewrite the integrand x^3\left(x^2+1\right)^8 in expanded form. Expand the integral \int\left(x^{19}+8x^{17}+28x^{15}+56x^{13}+70x^{11}+56x^{9}+28x^{7}+8x^{5}+x^3\right)dx into 9 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int x^{19}dx results in: \frac{x^{20}}{20}. The integral \int8x^{17}dx results in: \frac{4}{9}x^{18}.
Find the integral int(x^3(x^2+1)^8)dx
Final answer to the exercise
$\frac{x^{20}}{20}+\frac{4}{9}x^{18}+\frac{7}{4}x^{16}+4x^{14}+\frac{35}{6}x^{12}+\frac{28}{5}x^{10}+\frac{7}{2}x^{8}+\frac{4}{3}x^{6}+\frac{x^{4}}{4}+C_0$