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Popular Calculus >

integral of e^x-2^x

Solution

integral

e^{x} - 2^{x}

Solution

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

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int e^{x} d x - \int 2^{x} d x

\int e^{x} d x = e^{x}

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

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

Add a constant to the solution

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

Graph

Popular Examples

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

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

integral of t^2e^t

in t e g r a l t^{2} e^{t}

integral of 5y^2(e^x)^2

in t e g r a l 5 y^{2} (e^{x})^{2}

Frequently Asked Questions (FAQ)

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