Advertisements
Advertisements
प्रश्न
Choose the correct alternative from the following.
`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5 "dx"` =
विकल्प
`(-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
`int1/xlogxdx=...............`
(A)log(log x)+ c
(B) 1/2 (logx )2+c
(C) 2log x + c
(D) log x + c
If u and v are two functions of x then prove that
`intuvdx=uintvdx-int[du/dxintvdx]dx`
Hence evaluate, `int xe^xdx`
Integrate the function in x log 2x.
Integrate the function in x tan-1 x.
Integrate the function in x sec2 x.
Integrate the function in `e^x (1 + sin x)/(1+cos x)`.
Integrate the function in `((x- 3)e^x)/(x - 1)^3`.
Evaluate the following : `int x^3.tan^-1x.dx`
Evaluate the following : `int e^(2x).cos 3x.dx`
Choose the correct options from the given alternatives :
`int cos -(3)/(7)x*sin -(11)/(7)x*dx` =
Integrate the following with respect to the respective variable : `(sin^6θ + cos^6θ)/(sin^2θ*cos^2θ)`
Integrate the following w.r.t.x : `(1)/(xsin^2(logx)`
Integrate the following w.r.t.x : log (log x)+(log x)–2
Evaluate the following.
∫ x log x dx
Evaluate:
∫ (log x)2 dx
`int 1/sqrt(2x^2 - 5) "d"x`
`int sin4x cos3x "d"x`
Choose the correct alternative:
`int ("d"x)/((x - 8)(x + 7))` =
`int "e"^x int [(2 - sin 2x)/(1 - cos 2x)]`dx = ______.
If u and v ore differentiable functions of x. then prove that:
`int uv dx = u intv dx - int [(du)/(d) intv dx]dx`
Hence evaluate `intlog x dx`
`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`
`int(3x^2)/sqrt(1+x^3) dx = sqrt(1+x^3)+c`
`int1/(x+sqrt(x)) dx` = ______
Evaluate `int(1 + x + (x^2)/(2!))dx`
Evaluate:
`int e^(ax)*cos(bx + c)dx`
Evaluate:
`int (logx)^2 dx`
Prove that `int sqrt(x^2 - a^2)dx = x/2 sqrt(x^2 - a^2) - a^2/2 log(x + sqrt(x^2 - a^2)) + c`
Evaluate:
`inte^x "cosec" x(1 - cot x)dx`
Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate \[\int x\cos x\,dx.\]
