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Popular >

integral of 5x-5^x

Solution

\int 5 x - 5^{x} d x

Solution

\frac{5 x ^{2}}{2} - \frac{5 ^{x}}{ln ( 5 )} + C

Solution steps

\int 5 x - 5^{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 5 x d x - \int 5^{x} d x

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 5^{x} d x = \frac{5 ^{x}}{ln ( 5 )}

= \frac{5 x ^{2}}{2} - \frac{5 ^{x}}{ln ( 5 )}

Add a constant to the solution

= \frac{5 x ^{2}}{2} - \frac{5 ^{x}}{ln ( 5 )} + C

Graph

Popular Examples

integral of (e^{5x})/(4+e^{5x)}

\int \frac{e ^{5 x}}{4 + e ^{5 x}} d x

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

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\int 3 a x \cdot e^{- 2 b x} d x

integral of sqrt((2x-1)^2-9)

\int (2 x - 1)^{2} - 9 d x

Frequently Asked Questions (FAQ)

What is the integral of 5x-5^x ?
The integral of 5x-5^x is (5x^2)/2-(5^x)/(ln(5))+C