Final answer to the problem
$\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(\frac{13+\sqrt{5}}{2}+2n+2\right)}}{\left(\frac{13+\sqrt{5}}{2}+2n+2\right)\left(2n+1\right)!}+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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1
Rewrite the function $\sin\left(x\right)$ as it's representation in Maclaurin series expansion
Learn how to solve integrals with radicals problems step by step online.
$\int x^{\frac{13+\sqrt{5}}{2}}\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^n}{\left(2n+1\right)!}x^{\left(2n+1\right)}dx$
Learn how to solve integrals with radicals problems step by step online. Integrate int(x^((13+5^(1/2))/2)sin(x))dx. Rewrite the function \sin\left(x\right) as it's representation in Maclaurin series expansion. Bring the outside term x^{\frac{13+\sqrt{5}}{2}} inside the power serie. When multiplying exponents with same base we can add the exponents. We can rewrite the power series as the following.
Final answer to the problem
$\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(\frac{13+\sqrt{5}}{2}+2n+2\right)}}{\left(\frac{13+\sqrt{5}}{2}+2n+2\right)\left(2n+1\right)!}+C_0$
