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Popular >

integral of (2/3)^x

Solution

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

Solution

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

Solution steps

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

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

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

Simplify

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

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

Add a constant to the solution

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

Popular Examples

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

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

integral of (4x^2)/(x^2+1)

\int \frac{4 x ^{2}}{x ^{2} + 1} d x

integral of sqrt(x)sqrt((8x)^{3/2)+7}

\int x (8 x)^{\frac{3}{2}} + 7 d x

integral of ((x^2)/2)

\int (\frac{x ^{2}}{2}) d x

integral of 7x-x^2

\int 7 x - x^{2} d x

Frequently Asked Questions (FAQ)

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