What is the integral of (3x-1/x-7e^x+14e) ?

The integral of (3x-1/x-7e^x+14e) is (3x^2)/2-ln|x|-7e^x+14ex+C

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integral of (3x-1/x-7e^x+14e)

\int (3 x - \frac{1}{x} - 7 e^{x} + 14 e) d x

\frac{3 x ^{2}}{2} - ln ∣ x ∣ - 7 e^{x} + 14 e x + C

Solution steps

\int 3 x - \frac{1}{x} - 7 e^{x} + 14 e 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 x d x - \int \frac{1}{x} d x - \int 7 e^{x} d x + \int 14 e d x

\int 3 x d x = \frac{3 x ^{2}}{2}

\int \frac{1}{x} d x = ln ∣ x ∣

\int 7 e^{x} d x = 7 e^{x}

\int 14 e d x = 14 e x

= \frac{3 x ^{2}}{2} - ln ∣ x ∣ - 7 e^{x} + 14 e x

Add a constant to the solution

= \frac{3 x ^{2}}{2} - ln ∣ x ∣ - 7 e^{x} + 14 e x + C

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\frac{d}{d x} (x y + 1)

\frac{d}{d x} (3 (sin (2 x) cos (x) - sin^{3} (x)))

\int_{0}^{3} x x^{2} + 1 d x

\int \frac{1}{20 - y} d y

What is the integral of (3x-1/x-7e^x+14e) ?
The integral of (3x-1/x-7e^x+14e) is (3x^2)/2-ln|x|-7e^x+14ex+C