What is the integral of xe^{y^2} ?

The integral of xe^{y^2} is (e^{y^2}x^2)/2+C

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integral of xe^{y^2}

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

: \frac{x ^{2}}{2}

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Add a constant to the solution

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

\frac{d}{d x} ((x y)^{\frac{1}{2}})

cos (5 x)

\int \frac{1}{2 x + 5} d x

x \to 0 lim (x + 3)

\frac{d}{d x} (i e^{i x})