Final answer to the problem
$-\frac{1}{5}\sum_{n=0}^{\infty } \frac{\left(u+x^2\right)^nu}{n!}+C_1$
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Step-by-step Solution
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- Integrate by partial fractions
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1
The integral $-\int e^{\left(5t+x^2\right)}dt$ results in: $-\frac{1}{5}\sum_{n=0}^{\infty } \frac{1}{n!}\int\left(u+x^2\right)^ndu$
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$-\frac{1}{5}\sum_{n=0}^{\infty } \frac{1}{n!}\int\left(u+x^2\right)^ndu$
Learn how to solve integration techniques problems step by step online. Find the integral 3-int(e^(5t+x^2))dt. The integral -\int e^{\left(5t+x^2\right)}dt results in: -\frac{1}{5}\sum_{n=0}^{\infty } \frac{1}{n!}\int\left(u+x^2\right)^ndu. Gather the results of all integrals. The integral of a constant is equal to the constant times the integral's variable. Multiply the fraction by the term .
Final answer to the problem
$-\frac{1}{5}\sum_{n=0}^{\infty } \frac{\left(u+x^2\right)^nu}{n!}+C_1$
