What is the integral of (e^{x^2})/(x^3) ?

The integral of (e^{x^2})/(x^3) is -(e^{x^2})/(2x^2)+1/2 \Ei(x^2)+C

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integral of (e^{x^2})/(x^3)

\int \frac{e ^{x^{2}}}{x ^{3}} d x

- \frac{e ^{x^{2}}}{2 x ^{2}} + \frac{1}{2} Ei (x^{2}) + C

Solution steps

\int \frac{e ^{x^{2}}}{x ^{3}} d x

Apply Integration By Parts

: - \frac{e ^{x^{2}}}{2 x ^{2}} - \int - \frac{e ^{x^{2}}}{x} d x

= - \frac{e ^{x^{2}}}{2 x ^{2}} - \int - \frac{e ^{x^{2}}}{x} d x

\int - \frac{e ^{x^{2}}}{x} d x = - \frac{1}{2} Ei (x^{2})

= - \frac{e ^{x^{2}}}{2 x ^{2}} - (- \frac{1}{2} Ei (x^{2}))

Simplify

= - \frac{e ^{x^{2}}}{2 x ^{2}} + \frac{1}{2} Ei (x^{2})

Add a constant to the solution

= - \frac{e ^{x^{2}}}{2 x ^{2}} + \frac{1}{2} Ei (x^{2}) + C

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What is the integral of (e^{x^2})/(x^3) ?
The integral of (e^{x^2})/(x^3) is -(e^{x^2})/(2x^2)+1/2 \Ei(x^2)+C