Home
Class 12
MATHS
"If" int(dx)/((x^(2)-2x+10)^(2))=A("tan"...

`"If" int(dx)/((x^(2)-2x+10)^(2))=A("tan"^(-1)((x-1)/(3))+(f(x))/(x^(2)-2x+10))+C`,where, C is a constant of integration, then

A

`A=(1)/(27) and f(x) = 9(x-1)`

B

`A=(1)/(54 ) and f(x) =9(x-1)^2`

C

`A=(1)/(81) and f(x) = 3 (x-1)`

D

`A=(1)/(54) and f(x) =3 (x-1)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Similar Questions

Explore conceptually related problems

If int(dx)/((x^(2)+x+1)^(2))=atan^(-1)((2x+1)/(sqrt(3)))+b((2x+1)/(x^(2)+x+1))+C , x gt 0 where C is the constant of integration, then the value of 9(sqrt(3)a+b) is equal to __________.

If I=int(dx)/(x^(3)(x^(8)+1)^(3//4))=(lambda(1+x^(8))^((1)/(4)))/(x^(2))+c (where c is the constant of integration), then the value of lambda is equal to

int("sin"(5x)/(2))/("sin"(x)/(2))dx is equal to (where, C is a constant of integration)

int((f'(x)g(x)+f(x)g'(x)))/((1+(f(x)g(x))^(2)))dx is where C is constant of integration

If int x^(5)e^(-x^(2))dx = g(x)e^(-x^(2))+C , where C is a constant of integration, then g(-1) is equal to

If int (x+1)/(sqrt(2x-1))dx = f(x)sqrt(2x-1)+C , where C is a constant of integration, then f(x) is equal to

If I=int(tan^(-1)(e^(x)))/(e^(x)+e^(-x))dx=([tan^(-1)(f(x))]^(2))/(2)+C (where C is the constant of integration), then the range of y=f(x) AA x in R is

int ((x ^(2) -x+1)/(x ^(2) +1)) e ^(cot^(-1) (x))dx =f (x) .e ^(cot ^(-1)(x)) +C where C is constant of integration. Then f (x) is equal to:

If int(dx)/(x^(3)(1+x^(6))^(2/3))=xf(x)(1+x^(6))^(1/3)+C where, C is a constant of integration, then the function f(x) is equal to

if int x^(5)e^(-x^(2))dx=g(x)e^(-x^(2))+c where c is a constant of integration then g(-1) is equal to