∫dxx(x 2)(x #10;4)^2 By partial fractions, #10; #10; ∫( 132x + 1 #10;8(x 2) 3 32(x 4) + 1 8(x 4)^2 #10;)dx #10; #10; ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Integration of Piecewise Continuous Functions

∫dx/x x - 2 x...

Question

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

Open in App

Solution

$\int \frac{d x}{x (x - 2) {(x - 4)}^{2}}$
By partial fractions,

$\int (\frac{- 1}{32 x} + \frac{1}{8 (x - 2)} - \frac{3}{32 (x - 4)} + \frac{1}{8 {(x - 4)}^{2}}) d x$

$= \frac{- 1}{32} log x - \frac{1}{8 (x - 4)} + \frac{l o g (x - 2)}{8} - 3 \frac{l o g (x - 4)}{32} + C$

Suggest Corrections

Similar questions

x(x+1) + (x+2)(x+3) = 42

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

Solve the following quadratic equations :
(i) $3 (x^{2} - 4) = 5 x$
(ii) x(x + 1) + (x + 2) (x + 3) = 42

The value of the integral $\int (x^{2} + x) (x^{- 8} + 2 x^{- 9})^{1 / 10} d x$ is

y = x^{x} + \frac{1}{x^{x}}

\frac{d y}{d x} =

Join BYJU'S Learning Program