Final answer to the problem
$\sqrt{\pi }\mathrm{erf}\left(\sqrt{x}\right)-\sqrt{\pi }\mathrm{erf}\left(0\right)+C_0$
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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 exponent using the power rule $\frac{a^m}{a^n}=a^{m-n}$, where in this case $m=0$
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$2\int_{0}^{\sqrt{x}} e^{-b^2}db$
Learn how to solve problems step by step online. Find the integral 2int(1/(e^b^2))db&0&x^(1/2). Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. Rewrite the function e^{-b^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(b^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.
Final answer to the problem
$\sqrt{\pi }\mathrm{erf}\left(\sqrt{x}\right)-\sqrt{\pi }\mathrm{erf}\left(0\right)+C_0$
