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

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

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

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

e^{\frac{3}{2} x} + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = \frac{3}{2} x

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

Simplify

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

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

Add a constant to the solution

= e^{\frac{3}{2} x} + C

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