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
Evaluate the following:
`int x^2 sin 3x dx`
Evaluate the following:
`int sec^3x.dx`
Evaluate the following : `int x.sin^2x.dx`
Evaluate the following : `int x^2*cos^-1 x*dx`
Evaluate the following : `int cos sqrt(x).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:
sin (log x)
Integrate the following functions w.r.t. x : `x^2 .sqrt(a^2 - x^6)`
Integrate the following functions w.r.t. x : `(x + 1) sqrt(2x^2 + 3)`
Integrate the following functions w.r.t. x : `e^x .(1/x - 1/x^2)`
Choose the correct options from the given alternatives :
`int tan(sin^-1 x)*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)`
Evaluate the following.
∫ x log x dx
Evaluate the following.
`int x^2 e^4x`dx
Evaluate the following.
`int x^2 *e^(3x)`dx
Evaluate the following.
`int "e"^"x" "x - 1"/("x + 1")^3` dx
Evaluate the following.
`int "e"^"x" [(log "x")^2 + (2 log "x")/"x"]` dx
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
Evaluate: `int "dx"/("9x"^2 - 25)`
Evaluate: `int "e"^"x"/(4"e"^"2x" -1)` dx
`int ("e"^xlog(sin"e"^x))/(tan"e"^x) "d"x`
Choose the correct alternative:
`intx^(2)3^(x^3) "d"x` =
Evaluate `int 1/(x(x - 1)) "d"x`
∫ log x · (log x + 2) dx = ?
`int "e"^x int [(2 - sin 2x)/(1 - cos 2x)]`dx = ______.
Find the general solution of the differential equation: `e^((dy)/(dx)) = x^2`.
If `int(2e^(5x) + e^(4x) - 4e^(3x) + 4e^(2x) + 2e^x)/((e^(2x) + 4)(e^(2x) - 1)^2)dx = tan^-1(e^x/a) - 1/(b(e^(2x) - 1)) + C`, where C is constant of integration, then value of a + b is equal to ______.
If `int(x + (cos^-1 3x)^2)/sqrt(1 - 9x^2)dx = 1/α(sqrt(1 - 9x^2) + (cos^-1 3x)^β) + C`, where C is constant of integration , then (α + 3β) is equal to ______.
Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.
`intsqrt(1+x) dx` = ______
Evaluate:
`int1/(x^2 + 25)dx`
Evaluate the following.
`intx^3e^(x^2) dx`
Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3) dx`
`∫ sin^(−1)` xdx is equal to ______.
For the special integral \[\int e^x\left[f(x)+f'(x)\right]dx,\] what is the antiderivative?
