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Popular >

integral of 3^{5x}

Solution

\int 3^{5 x} d x

Solution

\frac{24 3 ^{x}}{5 ln ( 3 )} + C

Solution steps

\int 3^{5 x} d x

Simplify

3^{5 x} : 24 3^{x}

= \int 24 3^{x} d x

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

= \frac{24 3 ^{x}}{ln ( 243 )}

Simplify

ln (243) : 5 ln (3)

= \frac{24 3 ^{x}}{5 ln ( 3 )}

Add a constant to the solution

= \frac{24 3 ^{x}}{5 ln ( 3 )} + C

Popular Examples

3y^{''}+10y^'=0

3 y^{^{''}} + 10 y^{^{'}} = 0

(dy)/(dx)=x^6y^{-3}

\frac{d y}{d x} = x^{6} y^{- 3}

t^2(dy)/(dt)-t=1+y+ty,y(1)=5

t^{2} \frac{d y}{d t} - t = 1 + y + t y, y (1) = 5

area y=0.01x^2-3x+229,y=429-2x,x=0 area

y = 0.01 x^{2} - 3 x + 229, y = 429 - 2 x, x = 0

integral of 1/((1-sin(x)))

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

Frequently Asked Questions (FAQ)

What is the integral of 3^{5x} ?
The integral of 3^{5x} is (243^x)/(5ln(3))+C