What is the integral of (3e^x-5x) ?

The integral of (3e^x-5x) is 3e^x-(5x^2)/2+C

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integral of (3e^x-5x)

\int (3 e^{x} - 5 x) d x

3 e^{x} - \frac{5 x ^{2}}{2} + C

Solution steps

\int 3 e^{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 3 e^{x} d x - \int 5 x d x

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

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

= 3 e^{x} - \frac{5 x ^{2}}{2}

Add a constant to the solution

= 3 e^{x} - \frac{5 x ^{2}}{2} + C

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What is the integral of (3e^x-5x) ?
The integral of (3e^x-5x) is 3e^x-(5x^2)/2+C