What is the integral of xe^{(1+x^2)} ?

The integral of xe^{(1+x^2)} is 1/2 e^{1+x^2}+C

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integral of xe^{(1+x^2)}

\int x e^{(1 + x^{2})} d x

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

Solution steps

\int x e^{1 + x^{2}} 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 = 1 + x^{2}

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

Add a constant to the solution

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

5 x^{2} y^{^{'}} = y^{^{'}} + 5 x e^{- y}

\frac{\partial}{\partial x} (W \cdot L \cdot H (W, L, x))

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

\frac{d}{d x} (\frac{x ^{2} + 3}{x})

y = x^{2} sin^{6} (x) + x cos^{- 2} (x)

What is the integral of xe^{(1+x^2)} ?
The integral of xe^{(1+x^2)} is 1/2 e^{1+x^2}+C