What is the integral of (-13x+3)/((-4x+2)^2) ?

The integral of (-13x+3)/((-4x+2)^2) is -13(x/(4(-4x+2))+1/16 ln|-4x+2|)+3/(4(-4x+2))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (-13x+3)/((-4x+2)^2)

\int \frac{- 13 x + 3}{( - 4 x + 2 ) ^{2}} d x

- 13 (\frac{x}{4 ( - 4 x + 2 )} + \frac{1}{16} ln ∣ - 4 x + 2 ∣) + \frac{3}{4 ( - 4 x + 2 )} + C

Solution steps

\int \frac{- 13 x + 3}{( - 4 x + 2 ) ^{2}} d x

Expand

\frac{- 13 x + 3}{( - 4 x + 2 ) ^{2}} : - \frac{13 x}{( - 4 x + 2 ) ^{2}} + \frac{3}{( - 4 x + 2 ) ^{2}}

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{13 x}{( - 4 x + 2 ) ^{2}} d x + \int \frac{3}{( - 4 x + 2 ) ^{2}} d x

\int \frac{13 x}{( - 4 x + 2 ) ^{2}} d x = 13 (\frac{x}{4 ( - 4 x + 2 )} + \frac{1}{16} ln ∣ - 4 x + 2 ∣)

\int \frac{3}{( - 4 x + 2 ) ^{2}} d x = \frac{3}{4 ( - 4 x + 2 )}

= - 13 (\frac{x}{4 ( - 4 x + 2 )} + \frac{1}{16} ln ∣ - 4 x + 2 ∣) + \frac{3}{4 ( - 4 x + 2 )}

Add a constant to the solution

= - 13 (\frac{x}{4 ( - 4 x + 2 )} + \frac{1}{16} ln ∣ - 4 x + 2 ∣) + \frac{3}{4 ( - 4 x + 2 )} + C

\int (x^{2} - 2 x) e^{- x} d x

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

\int \frac{- 3}{2 - 3 m} d m

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

\int sin^{4} (π x) d x

What is the integral of (-13x+3)/((-4x+2)^2) ?
The integral of (-13x+3)/((-4x+2)^2) is -13(x/(4(-4x+2))+1/16 ln|-4x+2|)+3/(4(-4x+2))+C