What is the integral of 3(e^{3x}-e^x) ?

The integral of 3(e^{3x}-e^x) is e^{3x}-3e^x+C

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integral of 3(e^{3x}-e^x)

\int 3 (e^{3 x} - e^{x}) d x

e^{3 x} - 3 e^{x} + C

Solution steps

\int 3 (e^{3 x} - e^{x}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int e^{3 x} - e^{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

= 3 (\int e^{3 x} d x - \int e^{x} d x)

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

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

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

Simplify

3 (\frac{1}{3} e^{3 x} - e^{x}) : e^{3 x} - 3 e^{x}

= e^{3 x} - 3 e^{x}

Add a constant to the solution

= e^{3 x} - 3 e^{x} + C

\int (\frac{1}{x ^{13}}) d x

\frac{d}{d x} (x^{2} sin^{8} (x) + x cos^{- 5} (x))

- 3 (x)^{5} + 9 (x)^{3}, at x = - 1

4 x^{2}, 16 x

y^{^{'}} (x - 1) + y (x - 2) = 0

What is the integral of 3(e^{3x}-e^x) ?
The integral of 3(e^{3x}-e^x) is e^{3x}-3e^x+C