What is the integral of e^{sqrt(3s+9)} ?

The integral of e^{sqrt(3s+9)} is 2/3 (e^{sqrt(3s+9)}sqrt(3s+9)-e^{sqrt(3s+9)})+C

Popular >

integral of e^{sqrt(3s+9)}

\int e^{3 s + 9} d s

\frac{2}{3} (e^{3 s + 9} 3 s + 9 - e^{3 s + 9}) + C

Solution steps

\int e^{3 s + 9} d s

Apply u-substitution

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

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

Apply Integration By Parts

: e^{u} u - \int e^{u} d u

= \frac{2}{3} (e^{u} u - \int e^{u} d u)

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

= \frac{2}{3} (e^{u} u - e^{u})

Substitute back

u = 3 s + 9

= \frac{2}{3} (e^{3 s + 9} 3 s + 9 - e^{3 s + 9})

Add a constant to the solution

= \frac{2}{3} (e^{3 s + 9} 3 s + 9 - e^{3 s + 9}) + C

\int \frac{1}{sin ( x ) + 2} d x

\int e^{s i n (x)} \cdot sin (2 x) d x

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

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

\int \frac{1}{( sin ( x ) cos ( x ) )} d x

What is the integral of e^{sqrt(3s+9)} ?
The integral of e^{sqrt(3s+9)} is 2/3 (e^{sqrt(3s+9)}sqrt(3s+9)-e^{sqrt(3s+9)})+C