What is the integral of 3x^2-5x+7/x+2e^3 ?

The integral of 3x^2-5x+7/x+2e^3 is x^3-(5x^2)/2+7ln|x|+2e^3x+C

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integral of 3x^2-5x+7/x+2e^3

\int 3 x^{2} - 5 x + \frac{7}{x} + 2 e^{3} d x

x^{3} - \frac{5 x ^{2}}{2} + 7 ln ∣ x ∣ + 2 e^{3} x + C

Solution steps

\int 3 x^{2} - 5 x + \frac{7}{x} + 2 e^{3} 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^{2} d x - \int 5 x d x + \int \frac{7}{x} d x + \int 2 e^{3} d x

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

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

\int \frac{7}{x} d x = 7 ln ∣ x ∣

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

= x^{3} - \frac{5 x ^{2}}{2} + 7 ln ∣ x ∣ + 2 e^{3} x

Add a constant to the solution

= x^{3} - \frac{5 x ^{2}}{2} + 7 ln ∣ x ∣ + 2 e^{3} x + C

What is the integral of 3x^2-5x+7/x+2e^3 ?
The integral of 3x^2-5x+7/x+2e^3 is x^3-(5x^2)/2+7ln|x|+2e^3x+C