Advertisements
Advertisements
प्रश्न
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Advertisements
उत्तर
Let `I = int (4x + 2) sqrt(x^2 + x + 1)` dx
or `I = 2 int (2x + 1) sqrt ((x^2 + x + 1))` dx
Taking x2 + x + 1 = t
2x + 1 = dt
Hence, `I = 2 int sqrt t dt`
`= 2 int t^(1/2) dt = 2. 2/3 t^(3/2) + C`
`= 4/3 (x^2 + x + 1)^(3/2) + C`
APPEARS IN
संबंधित प्रश्न
Evaluate :`intxlogxdx`
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`(1+ log x)^2/x`
Write a value of
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Evaluate the following integrals : `int sin x/cos^2x dx`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
`int sqrt(1 + "x"^2) "dx"` =
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate `int "x - 1"/sqrt("x + 4")` dx
Evaluate: ∫ |x| dx if x < 0
`int 1/(cos x - sin x)` dx = _______________
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int 1/(xsin^2(logx)) "d"x`
`int (1 + x)/(x + "e"^(-x)) "d"x`
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
`int (cos x)/(1 - sin x) "dx" =` ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
If f'(x) = `x + 1/x`, then f(x) is ______.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
