Exercise
$\int2x^2sin\left(x^2\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int(2x^2sin(x^2))dx. The integral of a function times a constant (2) is equal to the constant times the integral of the function. Rewrite the function \sin\left(x^2\right) as it's representation in Maclaurin series expansion. Simplify \left(x^2\right)^{\left(2n+1\right)} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals 2n+1. Solve the product 2\left(2n+1\right).
Find the integral int(2x^2sin(x^2))dx
Final answer to the exercise
$2\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(5+4n\right)}}{\left(5+4n\right)\left(2n+1\right)!}+C_0$