Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate by parts
- Integrate by partial fractions
- Integrate by substitution
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
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Rewrite the integrand $\left(x^2+\sin\left(x\right)\right)^2$ in expanded form
Learn how to solve definite integrals problems step by step online.
$\int_{0}^{\pi }\left(x^{4}+2x^2\sin\left(x\right)+\sin\left(x\right)^{2}\right)dx$
Learn how to solve definite integrals problems step by step online. Integrate the function (x^2+sin(x))^2 from 0 to pi. Rewrite the integrand \left(x^2+\sin\left(x\right)\right)^2 in expanded form. Expand the integral \int_{0}^{\pi }\left(x^{4}+2x^2\sin\left(x\right)+\sin\left(x\right)^{2}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int2x^2\sin\left(x\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du.