What is the integral of (9/x+6/(x^4)) ?

The integral of (9/x+6/(x^4)) is 9ln|x|-2/(x^3)+C

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integral of (9/x+6/(x^4))

\int (\frac{9}{x} + \frac{6}{x ^{4}}) d x

9 ln ∣ x ∣ - \frac{2}{x ^{3}} + C

Solution steps

\int \frac{9}{x} + \frac{6}{x ^{4}} 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{9}{x} d x + \int \frac{6}{x ^{4}} d x

\int \frac{9}{x} d x = 9 ln ∣ x ∣

\int \frac{6}{x ^{4}} d x = - \frac{2}{x ^{3}}

= 9 ln ∣ x ∣ - \frac{2}{x ^{3}}

Add a constant to the solution

= 9 ln ∣ x ∣ - \frac{2}{x ^{3}} + C

(\frac{1}{x - 2})^{^{'}}

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

\frac{d}{d x} (\frac{( x ^{2} - 4 )}{x - 2})

\frac{1 + X}{1 - X}

\int e^{c o s (25 t)} sin (25 t) d t

What is the integral of (9/x+6/(x^4)) ?
The integral of (9/x+6/(x^4)) is 9ln|x|-2/(x^3)+C