Exercise
$\int\left(1-y\right)\left(2+y^2\right)dy$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int((1-y)(2+y^2))dy. Rewrite the integrand \left(1-y\right)\left(2+y^2\right) in expanded form. Expand the integral \int\left(2+y^2-2y-y^{3}\right)dy into 4 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int2dy results in: 2y. The integral \int y^2dy results in: \frac{y^{3}}{3}.
Find the integral int((1-y)(2+y^2))dy
Final answer to the exercise
$2y+\frac{y^{3}}{3}-y^2+\frac{-y^{4}}{4}+C_0$