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

The integral of 3e^x-5x^3+7+3/x is 3e^x-(5x^4)/4+7x+3ln|x|+C

Popular >

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

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

3 e^{x} - \frac{5 x ^{4}}{4} + 7 x + 3 ln ∣ x ∣ + C

Solution steps

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

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

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

\int 7 d x = 7 x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= 3 e^{x} - \frac{5 x ^{4}}{4} + 7 x + 3 ln ∣ x ∣

Add a constant to the solution

= 3 e^{x} - \frac{5 x ^{4}}{4} + 7 x + 3 ln ∣ x ∣ + C

\int x^{2} (5 x^{3} - 3)^{5} d x

\int x (x - 5)^{\frac{1}{2}} d x

\int e^{- \frac{x}{θ}} d x

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

\int b sin (x) cos (x) d x

What is the integral of 3e^x-5x^3+7+3/x ?
The integral of 3e^x-5x^3+7+3/x is 3e^x-(5x^4)/4+7x+3ln|x|+C