What is the integral of 3x*e^{1.5x^2} ?

The integral of 3x*e^{1.5x^2} is e^{1.5x^2}+C

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integral of 3x*e^{1.5x^2}

integral

3 x \cdot e^{1.5 x^{2}}

e^{1.5 x^{2}} + C

Solution steps

\int 3 x e^{1.5 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^{1.5 x^{2}} d x

Apply u-substitution

: \int \frac{e ^{u}}{3} d u

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = 1.5 x^{2}

= 3 \cdot \frac{1}{3} e^{1.5 x^{2}}

Simplify

3 \cdot \frac{1}{3} e^{1.5 x^{2}} : e^{1.5 x^{2}}

= e^{1.5 x^{2}}

Add a constant to the solution

= e^{1.5 x^{2}} + C

e^{x} \cdot cos^{2} (e^{x})

\frac{e ^{- 1}}{x ^{3}}

\frac{4}{x ^{3}}

\frac{r ^{2}}{( 1 + r ^{2} ) ^{2}}

\frac{( 4 + 12 x )}{4}

What is the integral of 3x*e^{1.5x^2} ?
The integral of 3x*e^{1.5x^2} is e^{1.5x^2}+C