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Popular >

integral of (3e^3)^x

Solution

\int (3 e^{3})^{x} d x

Solution

\frac{1}{ln ( 3 ) + 3} (3 e^{3})^{x} + C

Solution steps

\int (3 e^{3})^{x} d x

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

= \frac{( 3 e ^{3} ) ^{x}}{ln ( 3 e ^{3} )}

Simplify

\frac{( 3 e ^{3} ) ^{x}}{ln ( 3 e ^{3} )} : \frac{1}{ln ( 3 ) + 3} (3 e^{3})^{x}

= \frac{1}{ln ( 3 ) + 3} (3 e^{3})^{x}

Add a constant to the solution

= \frac{1}{ln ( 3 ) + 3} (3 e^{3})^{x} + C

Popular Examples

integral of 1/((x+3/2)sqrt(x^2+3x+45/4))

\int \frac{1}{( x + \frac{3}{2} ) x ^{2} + 3 x + \frac{45}{4}} d x

integral of 6/(5zsqrt(4z^4-9))

\int \frac{6}{5 z 4 z ^{4} - 9} d z

integral of (x^{(-3)/2}+x-7)/(sqrt(x))

\int \frac{x ^{\frac{- 3}{2}} + x - 7}{x} d x

integral of-(e^x)/(2+e^x)

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

integral of 1/(2^2+x^2)

\int \frac{1}{2 ^{2} + x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of (3e^3)^x ?
The integral of (3e^3)^x is 1/(ln(3)+3)(3e^3)^x+C