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

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

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

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

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

Solution steps

\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

x \to - 9 lim (\frac{x + 10}{x + 9})

\int (2 x + 3)^{- 3} d x

\frac{d}{d x} (\frac{5 x ^{2} + e ^{x}}{x ^{3}})

\frac{d}{d x} (\frac{1}{1 - 4 x})

\frac{d}{d x} (\frac{x ^{2}}{3 x - 4})

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