-x2-3-x3-2x2-x-2dx-A-1494log C - x-2 x-1 3-x-1 - then A is equal to-

I=∫ nbsp; x^ 2 3 x^ 3 2x^ 2 x+2 dx=∫ nbsp; x^ 2 3 ( x+1 ) ( x 1 ) ( x 2 ) nbsp; dx =∫ nbsp;( 1 3( x+1 ) nbsp; + 1 x 1 + 1 3( x ...

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Byju's Answer

Standard XII

Mathematics

Special Integrals - 1

∫x2-3/x3-2x2-...

Question

$\int \frac{x^{2} - 3}{x^{3} - 2 x^{2} - x + 2} d x = \frac{A}{1494} log (C ∣ ∣ ∣ ∣ \frac{(x - 2) {(x - 1)}^{3}}{x + 1} ∣ ∣ ∣ ∣)$ then A is equal to.

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Solution

$I = \int \frac{x^{2} - 3}{x^{3} - 2 x^{2} - x + 2} d x = \int \frac{x^{2} - 3}{(x + 1) (x - 1) (x - 2)} d x = \int (- \frac{1}{3 (x + 1)} + \frac{1}{x - 1} + \frac{1}{3 (x - 2)}) d x = - \frac{1}{3} log | x + I | + log | x - I | + \frac{1}{3} log | x - 2 | + c = (\frac{1}{3}) log {(| x + 1 |)}^{- 1} + \frac{1}{3} log {| x - 1 |}^{3} + \frac{1}{3} log | x - 2 | + \frac{1}{3} log c = \frac{1}{3} log C ∣ ∣ ∣ ∣ \frac{(x - 2) {(x - 1)}^{3}}{x + 1} ∣ ∣ ∣ ∣$
Therefore, $A = 498$

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Similar questions

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

will be equal to -

Question :

One of the factors of x⁵+x+1 is

(1) 2x² - x - 1

(2) x³ - x²+ 1

(3) x² - 2x² + 1

(4) x³ + x² + 1

(x+1) is a factor of the polynomial
(a) $x^{3} + x^{2} - x + 1$
(b) $x^{3} + 2 x^{2} - x - 2$
(c) $x^{3} + 2 x^{2} - x + 2$
(d) $x^{4} + x^{3} + x^{2} + 1$

Question 1
Which of the following is a quadratic equation?
(a) $x^{2} + 2 x + 1 = (4 - x)^{2} + 3$
(b) $- 2 x^{2} = (5 - x) (2 x - \frac{2}{5})$
(c) $(k + 1) x^{2} + \frac{3}{2} x = 7, w h e r e k = - 1$
(d) $x^{3} - x^{2} = (x - 1)^{3}$

Q. If dividend =

x^{4} + x^{3} - 2 x^{2} + x + 1

, divisor

= x - 1

and remainder

= 2

, then the quotient will be .

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∫x2−3x3−2x2−x+2dx=A1494log(C∣∣ ∣∣(x−2)(x−1)3x+1∣∣ ∣∣) then A is equal to.

I=∫x2−3x3−2x2−x+2dx=∫x2−3(x+1)(x−1)(x−2)dx=∫(−13(x+1)+1x−1+13(x−2))dx=−13log|x+I|+log|x−I|+13log|x−2|+c=(13)log(|x+1|)−1+13log|x−1|3+13log|x−2|+13logc=13logC∣∣ ∣∣(x−2)(x−1)3x+1∣∣ ∣∣Therefore, A=498

$\int \frac{x^{2} - 3}{x^{3} - 2 x^{2} - x + 2} d x = \frac{A}{1494} log (C ∣ ∣ ∣ ∣ \frac{(x - 2) {(x - 1)}^{3}}{x + 1} ∣ ∣ ∣ ∣)$ then A is equal to.