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Popular >

integral of 4x-2^x-e^{3x}

Solution

\int 4 x - 2^{x} - e^{3 x} d x

Solution

2 x^{2} - \frac{2 ^{x}}{ln ( 2 )} - \frac{1}{3} e^{3 x} + C

Solution steps

\int 4 x - 2^{x} - e^{3 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 4 x d x - \int 2^{x} d x - \int e^{3 x} d x

\int 4 x d x = 2 x^{2}

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

\int e^{3 x} d x = \frac{1}{3} e^{3 x}

= 2 x^{2} - \frac{2 ^{x}}{ln ( 2 )} - \frac{1}{3} e^{3 x}

Add a constant to the solution

= 2 x^{2} - \frac{2 ^{x}}{ln ( 2 )} - \frac{1}{3} e^{3 x} + C

Popular Examples

integral of (3x+3)/(x^2+x-2)

\int \frac{3 x + 3}{x ^{2} + x - 2} d x

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\int \frac{x ^{3} + 2 x ^{2} - 3 x + 1}{x ^{3} - 27} d x

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\int e^{w} d w

integral of X^{-2}

\int X^{- 2} d X

integral of (x+2)^9

\int (x + 2)^{9} d x

Frequently Asked Questions (FAQ)

What is the integral of 4x-2^x-e^{3x} ?
The integral of 4x-2^x-e^{3x} is 2x^2-(2^x)/(ln(2))-1/3 e^{3x}+C