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Popular Calculus >

integral of (e/2)^x

Solution

integral

(\frac{e}{2})^{x}

Solution

\frac{e ^{x}}{( 1 - ln ( 2 ) ) \cdot 2 ^{x}} + C

Solution steps

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

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

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

Simplify

\frac{( \frac{e}{2} ) ^{x}}{ln ( \frac{e}{2} )} : \frac{e ^{x}}{( 1 - ln ( 2 ) ) \cdot 2 ^{x}}

= \frac{e ^{x}}{( 1 - ln ( 2 ) ) \cdot 2 ^{x}}

Add a constant to the solution

= \frac{e ^{x}}{( 1 - ln ( 2 ) ) \cdot 2 ^{x}} + C

Graph

Popular Examples

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in t e g r a l csc^{4} (x)

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in t e g r a l \frac{x ^{3}}{( x ^{2} + 1 )}

Frequently Asked Questions (FAQ)

What is the integral of (e/2)^x ?
The integral of (e/2)^x is (e^x)/((1-ln(2))*2^x)+C