What is the integral of e^{(-2r)/a} ?

The integral of e^{(-2r)/a} is -a/2 e^{-(2r)/a}+C

Popular >

integral of e^{(-2r)/a}

integral

e^{\frac{- 2 r}{a}}

- \frac{a}{2} e^{- \frac{2 r}{a}} + C

Solution steps

\int e^{\frac{- 2 r}{a}} d r

Simplify

= \int e^{- \frac{2 r}{a}} d r

Apply u-substitution

: \int - \frac{a e ^{u}}{2} d u

= \int - \frac{a e ^{u}}{2} d u

Take the constant out:

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

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

Use the common integral:

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

= - \frac{a}{2} e^{u}

Substitute back

u = - \frac{2 r}{a}

= - \frac{a}{2} e^{- \frac{2 r}{a}}

Add a constant to the solution

= - \frac{a}{2} e^{- \frac{2 r}{a}} + C

\frac{( 1 + x )}{( 1 - x ) ^{2}}

\frac{1}{( x ^{2} + a )}

\frac{1}{( cos ^{2} ( x ) ( 1 - tan ( x ) ) ^{2} )}

\frac{7 x + 2}{1 - 25 x ^{2}}

a^{2} (e^{- a})^{2} x^{4}

What is the integral of e^{(-2r)/a} ?
The integral of e^{(-2r)/a} is -a/2 e^{-(2r)/a}+C