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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Apply the formula: $\int\sin\left(\theta \right)^n\cos\left(\theta \right)^mdx$$=\frac{-\sin\left(\theta \right)^{\left(n-1\right)}\cos\left(\theta \right)^{\left(m+1\right)}}{n+m}+\frac{n-1}{n+m}\int\sin\left(\theta \right)^{\left(n-2\right)}\cos\left(\theta \right)^mdx$, where $m=4$ and $n=4$
Learn how to solve trigonometric integrals problems step by step online.
$\frac{-\sin\left(x\right)^{3}\cos\left(x\right)^{5}}{4+4}+\frac{4-1}{4+4}\int\sin\left(x\right)^{2}\cos\left(x\right)^4dx$
Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(sin(x)^4cos(x)^4)dx. Apply the formula: \int\sin\left(\theta \right)^n\cos\left(\theta \right)^mdx=\frac{-\sin\left(\theta \right)^{\left(n-1\right)}\cos\left(\theta \right)^{\left(m+1\right)}}{n+m}+\frac{n-1}{n+m}\int\sin\left(\theta \right)^{\left(n-2\right)}\cos\left(\theta \right)^mdx, where m=4 and n=4. Simplify the expression. The integral \frac{3}{8}\int\sin\left(x\right)^{2}\cos\left(x\right)^4dx results in: \frac{3\cos\left(x\right)^{3}\sin\left(x\right)}{32}+\frac{9}{64}x+\frac{9}{128}\sin\left(2x\right)-\frac{1}{16}\cos\left(x\right)^{5}\sin\left(x\right)+\frac{-5\cos\left(x\right)^{3}\sin\left(x\right)}{64}-\frac{15}{64}\left(\frac{1}{2}x+\frac{1}{4}\sin\left(2x\right)\right). Gather the results of all integrals.
