Home
Class 12
MATHS
The integral int(3x^(13) + 2x^(11))/((2x...

The integral `int(3x^(13) + 2x^(11))/((2x^(4) + 3x^(2) +1)^(4))dx` is equal to `(x^(12))/(k(2x^(4) + 3x^(2) + 1)^3)+C`. The value of (k) is _________. (where C is a constant of integration)

Text Solution

Verified by Experts

The correct Answer is:
6
`I = int(3x^(13)+2x^(11))/((2x^(4) + 3x^(2) + 1))dx = int((3x^(13) + 2x^(11)))/(x^(16)(2+(3)/(x^(2))+(1)/(x^(4)))^(4))dx = int((3x^(-3) + 2x^(-5))dx)/((2+3x^(-2)+x^(-4))^(4))`
Put `2 + 3x^(-2) + x^(-4) = t, (-6x^(-3) - 4x^(-5))dx = dt`
`(3x^(-3) + 2x^(-5))dx = -(dt)/(2), I = (-1)/(2)int(dt)/(t^(4)) = (1)/(6)(1)/(t^(3))+c , I = (x^(12))/(6(2x^(4)+3x^(2)+1)^(3))+c`
Promotional Banner

Similar Questions

Explore conceptually related problems

The value of int(x dx)/((x+3)sqrt(x+1) is (where , c is the constant of integration )

The integral int(2x^(12)+5x^(9))/((x^(5)+x^(3)+1)^(3))dx is equal to (where C is a constant of integration)

What is int (x^(2) + 1)^((5)/(2))x dx equal to ? where c is a constant of integration

The integral int_(2)^(4)(log x^(2))/(log x^(2)+log(36-12x+x^(2)))dx is equal to: (1)2(2)4(3)1(4)6

The value of definite integral int_(1/3)^(2/3)(ln x)/(ln(x-x^(2)))dx is equal to :

The value of definite integral int_(1/3)^(2/3)(ln x)/(ln(x-x^(2)))dx is equal to

The value of definite integral int_(1/3)^(2/3)(ln x)/(ln(x-x^(2)))dx is equal to:

The integral int(sec^2x)/(3+4tan x)dx

The integral int(2x^(3)-1)/(x^(4)+x)dx is equal to (here C is a constant of intergration)

What is int (e^(x) (1 + x))/(cos^(2) (xe^(x))) dx equal to ? where c is a constant of integration