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

The integral of e^{x^2} x/3 is 1/6 e^{x^2}+C

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

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

\frac{1}{6} e^{x^{2}} + C

Solution steps

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

Take the constant out:

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

= \frac{1}{3} \cdot \int e^{x^{2}} x d x

Apply u-substitution

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

= \frac{1}{3} \cdot \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}{3} \cdot \frac{1}{2} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{3} \cdot \frac{1}{2} e^{u}

Substitute back

u = x^{2}

= \frac{1}{3} \cdot \frac{1}{2} e^{x^{2}}

Simplify

\frac{1}{3} \cdot \frac{1}{2} e^{x^{2}} : \frac{1}{6} e^{x^{2}}

= \frac{1}{6} e^{x^{2}}

Add a constant to the solution

= \frac{1}{6} e^{x^{2}} + C

n = 0 \sum \infty 2 \cdot 5^{n}

y^{^{'}} = \frac{y}{a} - 1

x \to 3 lim (2 3 x)

\int 5 e^{x} + 3 sin (x) d x

\int \frac{1}{x 4 x ^{2} + 49} d x

What is the integral of e^{x^2} x/3 ?
The integral of e^{x^2} x/3 is 1/6 e^{x^2}+C