The value of the integral ∫ (x2 - 4 x √x + 6 x - 4 √x + 1/x - 2 √x + 1) d x is equal to ( where c is constant of integration)

Question

The value of the integral ∫ (x2 - 4 x √x + 6 x - 4 √x + 1/x - 2 √x + 1) d x is equal to ( where c is constant of integration) (A) (x(3/2)/2)+x+c (B) (x2/2)-(4/3)x(3/2)+x+c (C) x(3/2)+(x/2)+c (D) (2/3)x(3/2)+c

Tardigrade Admin · Accepted Answer

Î=∫ ((√x - 1)4/(√x - 1)2)dx=∫ (√x - 1)2dx=∫ (x - 2 √x + 1)dx =(x2/2)-(4/3)x(3/2)+x+c

Q. The value of the integral $\int \frac{x ^{2} - 4 x x + 6 x - 4 x + 1}{x - 2 x + 1} d x$ is equal to ( where $c$ is constant of integration)

$\frac{x ^{\frac{3}{2}}}{2} + x + c$

$\frac{x ^{2}}{2} - \frac{4}{3} x^{\frac{3}{2}} + x + c$

$x^{\frac{3}{2}} + \frac{x}{2} + c$

$\frac{2}{3} x^{\frac{3}{2}} + c$

$I = \int \frac{( x - 1 ) ^{4}}{( x - 1 ) ^{2}} d x = \int (x - 1)^{2} d x = \int (x - 2 x + 1) d x$
$= \frac{x ^{2}}{2} - \frac{4}{3} x^{\frac{3}{2}} + x + c$

Q. The value of the integral ∫x−2x​+1x2−4xx​+6x−4x​+1​dx is equal to ( where c is constant of integration)

2x23​​+x+c

2x2​−34​x23​+x+c

x23​+2x​+c

32​x23​+c