Advertisements
Advertisements
प्रश्न
Choose the correct alternative from the following.
`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5 "dx"` =
पर्याय
`(-1)/"x + 1"` + c
`((-1)/"x + 1")^5` + c
log(x + 1) + c
log |x + 1|5 + c
Advertisements
उत्तर
`(-1)/"x + 1"` + c
Explanation:
= `int ("x + 1")^3/("x + 1")^5` dx
∵ (a + b)3 = a3 + 3a2b + 3ab2 + b3
(x + 1)3 = x3 + 3x2 + 3x + 1
= `1/((x + 1)^2) dx`
= `int (x + 1)^-2 . dx`
= `(x + 1)^(-2 + 1)/-2 + 1 + c`
= `(x + 1)^-1/-1 + c`
= `(-1)/(x + 1) + c`
`= (-1)/"x + 1"` + c
APPEARS IN
संबंधित प्रश्न
Integrate the function in x2 log x.
Integrate the function in e2x sin x.
Evaluate the following : `int x^3.tan^-1x.dx`
Evaluate the following : `int x^3.logx.dx`
Evaluate the following:
`int x.sin 2x. cos 5x.dx`
Integrate the following functions w.r.t. x:
sin (log x)
Integrate the following functions w.r.t. x : `sqrt((x - 3)(7 - x)`
Integrate the following functions w.r.t. x: `sqrt(x^2 + 2x + 5)`.
Integrate the following functions w.r.t. x : `((1 + sin x)/(1 + cos x)).e^x`
Integrate the following functions w.r.t. x : `log(1 + x)^((1 + x)`
Choose the correct options from the given alternatives :
`int (1)/(cosx - cos^2x)*dx` =
Evaluate the following.
∫ x log x dx
Evaluate the following.
`int "e"^"x" "x - 1"/("x + 1")^3` dx
Choose the correct alternative:
`intx^(2)3^(x^3) "d"x` =
`int ("d"x)/(x - x^2)` = ______
Evaluate `int 1/(x log x) "d"x`
`int log x * [log ("e"x)]^-2` dx = ?
Evaluate the following:
`int (sin^-1 x)/((1 - x)^(3/2)) "d"x`
Evaluate the following:
`int ((cos 5x + cos 4x))/(1 - 2 cos 3x) "d"x`
Evaluate the following:
`int_0^pi x log sin x "d"x`
Evaluate `int(3x-2)/((x+1)^2(x+3)) dx`
`int logx dx = x(1+logx)+c`
Evaluate:
`inte^x sinx dx`
Evaluate `int tan^-1x dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`intx^3 e^(x^2)dx`
Evaluate the following.
`intx^3/(sqrt(1 + x^4))dx`
