Final answer to the problem
$5\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(10n+6\right)}}{\left(10n+6\right)\left(2n+1\right)!}+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
- Integrate by substitution
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- Integrate using tabular integration
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- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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1
The integral of a function times a constant ($5$) is equal to the constant times the integral of the function
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$5\int\sin\left(x^5\right)dx$
Learn how to solve problems step by step online. Solve the trigonometric integral int(5sin(x^5))dx. The integral of a function times a constant (5) is equal to the constant times the integral of the function. Rewrite the function \sin\left(x^5\right) as it's representation in Maclaurin series expansion. Simplify \left(x^5\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 5 and n equals 2n+1. Solve the product 5\left(2n+1\right).
Final answer to the problem
$5\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(10n+6\right)}}{\left(10n+6\right)\left(2n+1\right)!}+C_0$
