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

The integral of 2e^{x/2} is 4e^{x/2}+C

Popular >

integral of 2e^{x/2}

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int e^{u} \cdot 2 d u

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

Take the constant out:

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

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

Use the common integral:

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

= 2 \cdot 2 e^{u}

Substitute back

u = \frac{x}{2}

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

Simplify

= 4 e^{\frac{x}{2}}

Add a constant to the solution

= 4 e^{\frac{x}{2}} + C

\int \frac{1}{x ( 6 x )} d x

x \to + 0 + lim (x^{12} ln (x))

\int x^{7} e^{x^{8}} d x

\int_{1}^{3} \frac{x ^{2} + 2}{4 x - x ^{2}} d x

\int \frac{3 x ^{2}}{x ^{3} + 1} d x