Final answer to the problem
$\frac{\sqrt{\pi }\mathrm{erf}\left(\sqrt{2}\right)x}{2}-\frac{\sqrt{\pi }\mathrm{erf}\left(2\right)x}{2}+C_0$
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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
Rewrite the function $e^{-t^2}$ as it's representation in Maclaurin series expansion
Learn how to solve integral calculus problems step by step online.
$x\int\sum_{2}^{\sqrt{2}}_{n=0}^{\infty } \frac{\left(-t^2\right)^n}{n!}dt$
Learn how to solve integral calculus problems step by step online. Find the integral xint(e^(-t^2))dt&2&2^(1/2). Rewrite the function e^{-t^2} 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^2\right)^n using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals n. We can rewrite the power series as the following.
Final answer to the problem
$\frac{\sqrt{\pi }\mathrm{erf}\left(\sqrt{2}\right)x}{2}-\frac{\sqrt{\pi }\mathrm{erf}\left(2\right)x}{2}+C_0$
