Advertisements
Advertisements
प्रश्न
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Advertisements
उत्तर
`int x^2(1 - 2/x)^2 dx`
= `int x^2 (1 - 4/x + 4/x^2)dx`
= `int (x^2 - 4x + 4)dx`
= `intx^2 dx - 4 int x dx + 4 int 1 dx`
= `x^3/(3) - 4(x^2/2) + 4x + c`
= `(1)/(3)x^3 - 2x^2 + 4x + c`.
APPEARS IN
संबंधित प्रश्न
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Evaluate the following integrals:
`int x/(x + 2).dx`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1
Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Evaluate `int 1/(x (x - 1))` dx
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
`int (sin4x)/(cos 2x) "d"x`
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int (7x + 9)^13 "d"x` ______ + c
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
`int x^3"e"^(x^2) "d"x`
`int (cos x)/(1 - sin x) "dx" =` ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate `int 1/("x"("x" - 1)) "dx"`
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate `int1/(x(x-1))dx`
