What is the integral of (3/x+4/(x^5)) ?

The integral of (3/x+4/(x^5)) is 3ln|x|-1/(x^4)+C

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integral of (3/x+4/(x^5))

\int (\frac{3}{x} + \frac{4}{x ^{5}}) d x

3 ln ∣ x ∣ - \frac{1}{x ^{4}} + C

Solution steps

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int \frac{4}{x ^{5}} d x = - \frac{1}{x ^{4}}

= 3 ln ∣ x ∣ - \frac{1}{x ^{4}}

Add a constant to the solution

= 3 ln ∣ x ∣ - \frac{1}{x ^{4}} + C

y = \frac{x ^{2}}{x}

\int \frac{1}{x} - \frac{2}{x ^{2}} + \frac{5}{x ^{3}} d x

\frac{d}{d t} (z (t))

f (x) = x^{2} e^{x} - 2 x e^{x} + 4 e^{x}

\int - 2 x cos (x) d x

What is the integral of (3/x+4/(x^5)) ?
The integral of (3/x+4/(x^5)) is 3ln|x|-1/(x^4)+C