Advertisements
Advertisements
प्रश्न
`int 1/(4x + 5x^(-11)) "d"x`
उत्तर
Let I = `int 1/(4x + 5x^(-11)) "d"x`
= `int 1/(4x + 5/x^11) "d"x`
= `int x^11/(4x^12 + 5) "d"x`
Put 4x12 + 5 = t
Differentiating w.r.t. x, we get
4(12)x11dx = dt
∴ x11dx = `1/48 "dt"`
∴ I = `1/48 int "dt"/"t"`
= `1/48 log |"t"| + "c"`
∴ I = `1/48 log |4x^12 + 5| + "c"`
APPEARS IN
संबंधित प्रश्न
Integrate : sec3 x w. r. t. x.
If u and v are two functions of x then prove that
`intuvdx=uintvdx-int[du/dxintvdx]dx`
Hence evaluate, `int xe^xdx`
Evaluate `int_0^(pi)e^2x.sin(pi/4+x)dx`
Integrate the function in x log 2x.
Integrate the function in x cos-1 x.
Integrate the function in x sec2 x.
Integrate the function in `(xe^x)/(1+x)^2`.
Integrate the function in `e^x (1 + sin x)/(1+cos x)`.
Integrate the function in `e^x (1/x - 1/x^2)`.
Integrate the function in `((x- 3)e^x)/(x - 1)^3`.
Integrate the function in e2x sin x.
`intx^2 e^(x^3) dx` equals:
Evaluate the following : `int x^2.log x.dx`
Evaluate the following : `int logx/x.dx`
Integrate the following functions w.r.t.x:
`e^-x cos2x`
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)`
Integrate the following functions w.r.t. x : [2 + cot x – cosec2x]ex
Integrate the following functions w.r.t. x : `((1 + sin x)/(1 + cos x)).e^x`
Integrate the following functions w.r.t. x : `e^x .(1/x - 1/x^2)`
Integrate the following functions w.r.t. x : cosec (log x)[1 – cot (log x)]
Choose the correct options from the given alternatives :
`int (1)/(x + x^5)*dx` = f(x) + c, then `int x^4/(x + x^5)*dx` =
Choose the correct options from the given alternatives :
`int (sin^m x)/(cos^(m+2)x)*dx` =
Choose the correct options from the given alternatives :
`int (x- sinx)/(1 - cosx)*dx` =
Choose the correct options from the given alternatives :
`int (1)/(cosx - cos^2x)*dx` =
Choose the correct options from the given alternatives :
`int sin (log x)*dx` =
Integrate the following with respect to the respective variable : `(3 - 2sinx)/(cos^2x)`
Integrate the following with respect to the respective variable : cos 3x cos 2x cos x
Integrate the following w.r.t.x : `(1)/(xsin^2(logx)`
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Solve the following differential equation.
(x2 − yx2 ) dy + (y2 + xy2) dx = 0
Evaluate the following.
∫ x log x dx
Evaluate the following.
`int "x"^2 "e"^"4x"`dx
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
Evaluate: Find the primitive of `1/(1 + "e"^"x")`
Evaluate: `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
Evaluate: `int "e"^"x"/(4"e"^"2x" -1)` dx
`int (sinx)/(1 + sin x) "d"x`
`int ("d"x)/(x - x^2)` = ______
`int(x + 1/x)^3 dx` = ______.
`int (x^2 + x - 6)/((x - 2)(x - 1)) "d"x` = x + ______ + c
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`
`int "e"^x x/(x + 1)^2 "d"x`
`int log x * [log ("e"x)]^-2` dx = ?
The value of `int "e"^(5x) (1/x - 1/(5x^2)) "d"x` is ______.
`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.
Evaluate the following:
`int (sin^-1 x)/((1 - x)^(3/2)) "d"x`
Evaluate the following:
`int_0^1 x log(1 + 2x) "d"x`
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`
Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`
`int 1/sqrt(x^2 - a^2)dx` = ______.
`int(logx)^2dx` equals ______.
`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.
`int_0^1 x tan^-1 x dx` = ______.
Find `int e^x ((1 - sinx)/(1 - cosx))dx`.
Solution of the equation `xdy/dx=y log y` is ______
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate `int(1 + x + (x^2)/(2!))dx`
Evaluate:
`int e^(ax)*cos(bx + c)dx`
Evaluate `int (1 + x + x^2/(2!))dx`
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)`dx
