What is the integral of ((4x-7))/(x^2-6x+13) ?

The integral of ((4x-7))/(x^2-6x+13) is 5/2 arctan(1/2 (x-3))+2ln|x^2-6x+13|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((4x-7))/(x^2-6x+13)

\int \frac{( 4 x - 7 )}{x ^{2} - 6 x + 13} d x

\frac{5}{2} arctan (\frac{1}{2} (x - 3)) + 2 ln x^{2} - 6 x + 13 + C

Solution steps

\int \frac{4 x - 7}{x ^{2} - 6 x + 13} d x

Apply Integration By Parts

: \frac{1}{2} arctan (\frac{1}{2} (x - 3)) (4 x - 7) - \int 2 arctan (\frac{1}{2} (x - 3)) d x

= \frac{1}{2} arctan (\frac{1}{2} (x - 3)) (4 x - 7) - \int 2 arctan (\frac{1}{2} (x - 3)) d x

\int 2 arctan (\frac{1}{2} (x - 3)) d x = 2 (x arctan (\frac{1}{2} (x - 3)) - ln x^{2} - 6 x + 13 - 3 arctan (\frac{1}{2} (x - 3)))

= \frac{1}{2} arctan (\frac{1}{2} (x - 3)) (4 x - 7) - 2 (x arctan (\frac{1}{2} (x - 3)) - ln x^{2} - 6 x + 13 - 3 arctan (\frac{1}{2} (x - 3)))

Simplify

\frac{1}{2} arctan (\frac{1}{2} (x - 3)) (4 x - 7) - 2 (x arctan (\frac{1}{2} (x - 3)) - ln x^{2} - 6 x + 13 - 3 arctan (\frac{1}{2} (x - 3))) : \frac{5}{2} arctan (\frac{1}{2} (x - 3)) + 2 ln x^{2} - 6 x + 13

= \frac{5}{2} arctan (\frac{1}{2} (x - 3)) + 2 ln x^{2} - 6 x + 13

Add a constant to the solution

= \frac{5}{2} arctan (\frac{1}{2} (x - 3)) + 2 ln x^{2} - 6 x + 13 + C

- \frac{7}{x ^{2}}

y = 8 - x^{2}, y = x^{2}, x = - 3, x = 3

(x^{2} + 4) d y = (2 x - 8 x y) d x

\int - \frac{2}{πn} cos (\frac{πn}{2} x) d x

\frac{d y}{d x} = \frac{7 x ^{2}}{5 y ^{2}}

What is the integral of ((4x-7))/(x^2-6x+13) ?
The integral of ((4x-7))/(x^2-6x+13) is 5/2 arctan(1/2 (x-3))+2ln|x^2-6x+13|+C