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Popular >

integral of 3^{3x}

Solution

\int 3^{3 x} d x

Solution

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

Solution steps

\int 3^{3 x} d x

Simplify

3^{3 x} : 2 7^{x}

= \int 2 7^{x} d x

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

= \frac{2 7 ^{x}}{ln ( 27 )}

Simplify

\frac{2 7 ^{x}}{ln ( 27 )} : \frac{3 ^{3 x - 1}}{ln ( 3 )}

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

Add a constant to the solution

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

Popular Examples

integral of sec(7x)

\int sec (7 x) d x

derivative of (x^3-2tan(x))

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

integral of (x^6e^{x^7})

\int (x^{6} e^{x^{7}}) d x

integral of (8x+12)/(x*(x^2+4))

\int \frac{8 x + 12}{x \cdot ( x ^{2} + 4 )} d x

(\partial)/(\partial x)(xsqrt(1+y^3))

\frac{\partial}{\partial x} (x 1 + y^{3})

Frequently Asked Questions (FAQ)

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