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Popular >

integral of (3/2)^x

Solution

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

Solution

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

Solution steps

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

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

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

Simplify

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

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

Add a constant to the solution

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

Popular Examples

derivative of 3x^7-7x^3+21x^2

\frac{d}{d x} (3 x^{7} - 7 x^{3} + 21 x^{2})

integral of 9sec^4(x)

\int 9 sec^{4} (x) d x

derivative of 5x^4-3x^2+1/(sqrt(x)-7)

\frac{d}{d x} (5 x^{4} - 3 x^{2} + \frac{1}{x} - 7)

integral of 1/(3+3cos(x))

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

(\partial)/(\partial x)(ln(xcos(y)))

\frac{\partial}{\partial x} (ln (x cos (y)))

Frequently Asked Questions (FAQ)

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