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
Evaluate `int_0^(pi)e^2x.sin(pi/4+x)dx`
Integrate the function in x cos-1 x.
Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.
Integrate the function in `e^x (1 + sin x)/(1+cos x)`.
`intx^2 e^(x^3) dx` equals:
Evaluate the following : `int x^3.tan^-1x.dx`
Evaluate the following : `int (t.sin^-1 t)/sqrt(1 - t^2).dt`
Evaluate the following : `int cos sqrt(x).dx`
Evaluate the following : `int x.cos^3x.dx`
Evaluate the following:
`int x.sin 2x. cos 5x.dx`
Evaluate the following : `int cos(root(3)(x)).dx`
Integrate the following functions w.r.t. x : `sqrt((x - 3)(7 - x)`
Integrate the following functions w.r.t. x : `sec^2x.sqrt(tan^2x + tan x - 7)`
Choose the correct options from the given alternatives :
`int (log (3x))/(xlog (9x))*dx` =
Integrate the following with respect to the respective variable : `t^3/(t + 1)^2`
Integrate the following with respect to the respective variable : `(3 - 2sinx)/(cos^2x)`
Integrate the following with respect to the respective variable : `(sin^6θ + cos^6θ)/(sin^2θ*cos^2θ)`
Integrate the following with respect to the respective variable : cos 3x cos 2x cos x
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`
Integrate the following w.r.t.x : log (x2 + 1)
Choose the correct alternative from the following.
`int (1 - "x")^(-2) "dx"` =
`int (cos2x)/(sin^2x cos^2x) "d"x`
`int ("e"^xlog(sin"e"^x))/(tan"e"^x) "d"x`
`int sqrt(tanx) + sqrt(cotx) "d"x`
Choose the correct alternative:
`int ("d"x)/((x - 8)(x + 7))` =
State whether the following statement is True or False:
If `int((x - 1)"d"x)/((x + 1)(x - 2))` = A log|x + 1| + B log|x – 2|, then A + B = 1
`int_0^1 x tan^-1 x dx` = ______.
Evaluate:
`int((1 + sinx)/(1 + cosx))e^x dx`
Evaluate the following.
`intx^3 e^(x^2)dx`
