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

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

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integral of e^{3/2 x}

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

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

Solution steps

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

Apply u-substitution

: \int e^{u} \frac{2}{3} d u

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

Use the common integral:

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

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

Substitute back

u = \frac{3}{2} x

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

Add a constant to the solution

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

t \frac{d y}{d t} + y = t^{2}

\int \frac{t}{t ^{2} + 1} d t

n = 1 \sum \infty (n + 1) x^{n}

\frac{ln ( x )}{x ^{2}}

x \to 0 + lim (\frac{2 ^{x}}{3 ^{x}})

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