What is the integral of 3xe^{0.5x^2} ?

The integral of 3xe^{0.5x^2} is 3e^{0.5x^2}+C

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integral of 3xe^{0.5x^2}

\int 3 x e^{0.5 x^{2}} d x

3 e^{0.5 x^{2}} + C

Solution steps

\int 3 x e^{0.5 x^{2}} d x

Take the constant out:

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

= 3 \cdot \int x e^{0.5 x^{2}} d x

Apply u-substitution

: \int e^{u} d u

= 3 \cdot \int e^{u} d u

Use the common integral:

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

= 3 e^{u}

Substitute back

u = 0.5 x^{2}

= 3 e^{0.5 x^{2}}

Add a constant to the solution

= 3 e^{0.5 x^{2}} + C

\int (20 x + 9) d x

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\frac{d}{d x} (x^{2} - 9)

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What is the integral of 3xe^{0.5x^2} ?
The integral of 3xe^{0.5x^2} is 3e^{0.5x^2}+C