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

The integral of 3^{x+2} is (3^{x+2})/(ln(3))+C

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integral of 3^{x+2}

\int 3^{x + 2} d x

\frac{3 ^{x + 2}}{ln ( 3 )} + C

Solution steps

\int 3^{x + 2} d x

Simplify

3^{x + 2} : 3^{x} \cdot 3^{2}

= \int 3^{x} \cdot 3^{2} d x

Take the constant out:

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

= 3^{2} \cdot \int 3^{x} d x

Simplify

= 9 \cdot \int 3^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= 9 \cdot \frac{3 ^{x}}{ln ( 3 )}

Simplify

9 \cdot \frac{3 ^{x}}{ln ( 3 )} : \frac{3 ^{x + 2}}{ln ( 3 )}

= \frac{3 ^{x + 2}}{ln ( 3 )}

Add a constant to the solution

= \frac{3 ^{x + 2}}{ln ( 3 )} + C

(sin (x) + cos (x))^{^{'}}

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

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

\frac{\partial}{\partial x} (- \frac{a}{x})

y = x^{2} - 8 x, (3, - 15)

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