Final answer to the problem
$\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nt^{\left(8n+1\right)}}{\left(8n+1\right)\left(n!\right)}+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
- Integrate by substitution
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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
Rewrite the function $e^{-t^8}$ as it's representation in Maclaurin series expansion
Learn how to solve integrals of exponential functions problems step by step online.
$\int\sum_{n=0}^{\infty } \frac{\left(-t^8\right)^n}{n!}dt$
Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(e^(-t^8))dt. Rewrite the function e^{-t^8} as it's representation in Maclaurin series expansion. The power of a product is equal to the product of it's factors raised to the same power. Simplify \left(t^8\right)^n using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 8 and n equals n. We can rewrite the power series as the following.
Final answer to the problem
$\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nt^{\left(8n+1\right)}}{\left(8n+1\right)\left(n!\right)}+C_0$
