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
Prove that: `int sqrt(a^2 - x^2) * dx = x/2 * sqrt(a^2 - x^2) + a^2/2 * sin^-1(x/a) + c`
Integrate the function in x log x.
Integrate the function in x2 log x.
Integrate the function in x sin−1 x.
Evaluate the following: `int x.sin^-1 x.dx`
Evaluate the following : `int x^2*cos^-1 x*dx`
Evaluate the following : `int(sin(logx)^2)/x.log.x.dx`
Integrate the following functions w.r.t.x:
`e^-x cos2x`
Integrate the following functions w.r.t. x : `sqrt(2x^2 + 3x + 4)`
Integrate the following functions w.r.t. x : `[x/(x + 1)^2].e^x`
Integrate the following w.r.t.x : `log (1 + cosx) - xtan(x/2)`
Integrate the following w.r.t.x : log (log x)+(log x)–2
Evaluate the following.
∫ x log x dx
Evaluate the following.
`int (log "x")/(1 + log "x")^2` dx
Choose the correct alternative from the following.
`int (1 - "x")^(-2) "dx"` =
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
Evaluate `int 1/(4x^2 - 1) "d"x`
Find `int_0^1 x(tan^-1x) "d"x`
Evaluate the following:
`int_0^pi x log sin x "d"x`
Find the general solution of the differential equation: `e^((dy)/(dx)) = x^2`.
Solve: `int sqrt(4x^2 + 5)dx`
`int(logx)^2dx` equals ______.
If `int (f(x))/(log(sin x))dx` = log[log sin x] + c, then f(x) is equal to ______.
Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.
Find `int e^x ((1 - sinx)/(1 - cosx))dx`.
Find: `int e^(x^2) (x^5 + 2x^3)dx`.
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4))dx`
`int (sin^-1 sqrt(x) + cos^-1 sqrt(x))dx` = ______.
Evaluate the following.
`intx^3 e^(x^2) dx`
