What is the integral of e^{x^2}*x ?

The integral of e^{x^2}*x is 1/2 e^{x^2}+C

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integral of e^{x^2}*x

\int e^{x^{2}} \cdot x d x

\frac{1}{2} e^{x^{2}} + C

Solution steps

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

Apply u-substitution

: \int \frac{e ^{u}}{2} d u

= \int \frac{e ^{u}}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= \frac{1}{2} e^{u}

Substitute back

u = x^{2}

= \frac{1}{2} e^{x^{2}}

Add a constant to the solution

= \frac{1}{2} e^{x^{2}} + C

(2 y - 2) \frac{d y}{d x} = 3 x^{2} + 4 x + 2

\frac{\partial}{\partial x} (9 sin (x y))

\int - 2 tan^{2} (x) d x

\frac{\partial}{\partial x} (x y^{2} + x^{2} y)

x \to 0 + lim ((2 x)^{3 x})