What is the integral of ((x+8)^2)/(x^2) ?

The integral of ((x+8)^2)/(x^2) is x+16ln|x|-(64)/x+C

Popular >

integral of ((x+8)^2)/(x^2)

\int \frac{( x + 8 ) ^{2}}{x ^{2}} d x

x + 16 ln ∣ x ∣ - \frac{64}{x} + C

Solution steps

\int \frac{( x + 8 ) ^{2}}{x ^{2}} d x

Expand

\frac{( x + 8 ) ^{2}}{x ^{2}} : 1 + \frac{16}{x} + \frac{64}{x ^{2}}

= \int 1 + \frac{16}{x} + \frac{64}{x ^{2}} 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 1 d x + \int \frac{16}{x} d x + \int \frac{64}{x ^{2}} d x

\int 1 d x = x

\int \frac{16}{x} d x = 16 ln ∣ x ∣

\int \frac{64}{x ^{2}} d x = - \frac{64}{x}

= x + 16 ln ∣ x ∣ - \frac{64}{x}

Add a constant to the solution

= x + 16 ln ∣ x ∣ - \frac{64}{x} + C

\int (x sin (x^{2}) + tan^{2} (x)) d x

\int e^{x} sin (nπ x) d x

\int x + 1 (x + 2) d x

\int (6 x^{2} + 8 x - sin (x)) d x

\int \frac{6 x + 4}{1 + ( 3 x + 2 ) ^{4}} d x

What is the integral of ((x+8)^2)/(x^2) ?
The integral of ((x+8)^2)/(x^2) is x+16ln|x|-(64)/x+C