Final answer to the problem
$\sum_{n=0}^{\infty } \frac{\left(x^{\left(2n+1\right)}\right)\left(2n\right)!}{2^{2n}n!^2\left(2n+1\right)^2}+C_0$
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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 $\arcsin\left(x\right)$ as it's representation in Maclaurin series expansion
$\int\frac{\sum_{n=0}^{\infty } \frac{\left(2n\right)!}{2^{2n}n!^2\left(2n+1\right)}x^{\left(2n+1\right)}}{x}dx$
Learn how to solve integral calculus problems step by step online.
$\int\frac{\sum_{n=0}^{\infty } \frac{\left(2n\right)!}{2^{2n}n!^2\left(2n+1\right)}x^{\left(2n+1\right)}}{x}dx$
Learn how to solve integral calculus problems step by step online. Find the integral int(arcsin(x)/x)dx. Rewrite the function \arcsin\left(x\right) as it's representation in Maclaurin series expansion. Bring the denominator x inside the power serie. Simplify the expression. We can rewrite the power series as the following.
Final answer to the problem
$\sum_{n=0}^{\infty } \frac{\left(x^{\left(2n+1\right)}\right)\left(2n\right)!}{2^{2n}n!^2\left(2n+1\right)^2}+C_0$
