What is the integral of ((-4x-4x^5)/(x^2)+5e^{7x}) ?

The integral of ((-4x-4x^5)/(x^2)+5e^{7x}) is -x^4-4ln|x|+5/7 e^{7x}+C

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integral of ((-4x-4x^5)/(x^2)+5e^{7x})

\int (\frac{- 4 x - 4 x ^{5}}{x ^{2}} + 5 e^{7 x}) d x

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

Solution steps

\int \frac{- 4 x - 4 x ^{5}}{x ^{2}} + 5 e^{7 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 \frac{- 4 x - 4 x ^{5}}{x ^{2}} d x + \int 5 e^{7 x} d x

\int \frac{- 4 x - 4 x ^{5}}{x ^{2}} d x = - x^{4} - 4 ln ∣ x ∣

\int 5 e^{7 x} d x = \frac{5}{7} e^{7 x}

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

Add a constant to the solution

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

What is the integral of ((-4x-4x^5)/(x^2)+5e^{7x}) ?
The integral of ((-4x-4x^5)/(x^2)+5e^{7x}) is -x^4-4ln|x|+5/7 e^{7x}+C