Advertisements
Advertisements
प्रश्न
Integrate the function in tan-1 x.
Advertisements
उत्तर
Let `I = int tan^-1 x dx`
`= int tan^-1 x. 1 dx`
Put `u = tan^-1 x, v = 1`
`int uv dx = u int v dx - int ((du)/dx int v dx) dx`
`I= int tan^-1 x. 1`
`(tan^-1 x) int 1 dx - (d/dx (tan^-1 x) int dx) dx`
`= x tan^-1 x - int 1/(1 + x^2) . x dx`
`= x tan^-1 x - 1/2 int (2x)/(1 + x^2) dx`
Put 1 + x2 = t, and dx = dt
`= x tan^-1 x - 1/2 int dt/t`
`= x tan^-1 x - 1/2 log t + C`
`= x tan^1 - 1/2 log (1 + x^2) + 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`
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^2e^x`.
Integrate the function in x sin−1 x.
Integrate the function in x tan-1 x.
Integrate the function in `(xe^x)/(1+x)^2`.
Integrate the function in `sin^(-1) ((2x)/(1+x^2))`.
`int e^x sec x (1 + tan x) dx` equals:
Find :
`∫(log x)^2 dx`
Evaluate the following:
`int sec^3x.dx`
Evaluate the following : `int sin θ.log (cos θ).dθ`
Integrate the following functions w.r.t. x : `e^(2x).sin3x`
Integrate the following functions w.r.t. x: `sqrt(x^2 + 2x + 5)`.
Integrate the following functions w.r.t. x : `e^x/x [x (logx)^2 + 2 (logx)]`
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 cos -(3)/(7)x*sin -(11)/(7)x*dx` =
Integrate the following w.r.t.x : `(1)/(xsin^2(logx)`
`int ("x" + 1/"x")^3 "dx"` = ______
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
Evaluate: `int "e"^"x"/(4"e"^"2x" -1)` dx
`int sqrt(tanx) + sqrt(cotx) "d"x`
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/(x(x - 1)) "d"x`
Evaluate the following:
`int (sin^-1 x)/((1 - x)^(3/2)) "d"x`
State whether the following statement is true or false.
If `int (4e^x - 25)/(2e^x - 5)` dx = Ax – 3 log |2ex – 5| + c, where c is the constant of integration, then A = 5.
`int 1/sqrt(x^2 - a^2)dx` = ______.
Solve: `int sqrt(4x^2 + 5)dx`
`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.
Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.
Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.
Solution of the equation `xdy/dx=y log y` is ______
Evaluate the following.
`int x^3 e^(x^2) dx`
`int1/(x+sqrt(x)) dx` = ______
Evaluate `int(1 + x + (x^2)/(2!))dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
