Final answer to the problem
$\sum_{n=0}^{\infty } \frac{5^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0$
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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 $e^{5x^2}$ as it's representation in Maclaurin series expansion
Learn how to solve integrals of exponential functions problems step by step online.
$\int\sum_{n=0}^{\infty } \frac{\left(5x^2\right)^n}{n!}dx$
Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(e^(5x^2))dx. Rewrite the function e^{5x^2} as it's representation in Maclaurin series expansion. We can rewrite the power series as the following. The power of a product is equal to the product of it's factors raised to the same power. The integral of a function times a constant (5^n) is equal to the constant times the integral of the function.
Final answer to the problem
$\sum_{n=0}^{\infty } \frac{5^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0$
