What is the integral of 20(e^{3/4 x}-e^{2x}) ?

The integral of 20(e^{3/4 x}-e^{2x}) is 20(4/3 e^{3/4 x}-1/2 e^{2x})+C

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integral of 20(e^{3/4 x}-e^{2x})

\int 20 (e^{\frac{3}{4} x} - e^{2 x}) d x

20 (\frac{4}{3} e^{\frac{3}{4} x} - \frac{1}{2} e^{2 x}) + C

Solution steps

\int 20 (e^{\frac{3}{4} x} - e^{2 x}) d x

Take the constant out:

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

= 20 \cdot \int e^{\frac{3}{4} x} - e^{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

= 20 (\int e^{\frac{3}{4} x} d x - \int e^{2 x} d x)

\int e^{\frac{3}{4} x} d x = \frac{4}{3} e^{\frac{3}{4} x}

\int e^{2 x} d x = \frac{1}{2} e^{2 x}

= 20 (\frac{4}{3} e^{\frac{3}{4} x} - \frac{1}{2} e^{2 x})

Add a constant to the solution

= 20 (\frac{4}{3} e^{\frac{3}{4} x} - \frac{1}{2} e^{2 x}) + C

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What is the integral of 20(e^{3/4 x}-e^{2x}) ?
The integral of 20(e^{3/4 x}-e^{2x}) is 20(4/3 e^{3/4 x}-1/2 e^{2x})+C