Advertisements
Advertisements
प्रश्न
Integrate the function in x tan-1 x.
Advertisements
उत्तर
Let `I = int x tan^-1 x dx`
`= tan^-1 x int x dx - int [(d/dx(tan^-1 x)) int (x dx)] dx`
`= tan^-1 x (x^2/2) - int 1/ (1 + x^2) * x^2/2 dx`
`= x^2/2 tan^-1 x - 1/2 int x^2/ (x^2 + 1) dx`
`= x^2/2 tan^-1 x - 1/2 int (x^2 + 1 - 1)/ (1 + x^2) dx`
`= x^2/2 tan^-1 x - 1/2 int (1 - 1/(1 + x^2)) dx`
`= x^2/2 tan^-1 x - 1/2 (x - tan^-1 x) + C`
`= x^2/2 tan^-1 x - 1/2 x + 1/2 tan^-1 x + C`
APPEARS IN
संबंधित प्रश्न
Integrate : sec3 x w. r. t. x.
Integrate the function in x log 2x.
Evaluate the following:
`int x tan^-1 x . dx`
Evaluate the following : `int x.sin^2x.dx`
Evaluate the following : `int cos sqrt(x).dx`
Evaluate the following: `int logx/x.dx`
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)`
Choose the correct options from the given alternatives :
`int [sin (log x) + cos (log x)]*dx` =
Integrate the following w.r.t.x : `log (1 + cosx) - xtan(x/2)`
Evaluate the following.
`int x^2 *e^(3x)`dx
Evaluate: `int "dx"/("9x"^2 - 25)`
Evaluate: `int "dx"/(5 - 16"x"^2)`
`int sqrt(tanx) + sqrt(cotx) "d"x`
`int(x + 1/x)^3 dx` = ______.
`int 1/(x^2 - "a"^2) "d"x` = ______ + c
`int"e"^(4x - 3) "d"x` = ______ + c
Evaluate `int 1/(4x^2 - 1) "d"x`
`int log x * [log ("e"x)]^-2` dx = ?
The value of `int "e"^(5x) (1/x - 1/(5x^2)) "d"x` is ______.
Evaluate the following:
`int ((cos 5x + cos 4x))/(1 - 2 cos 3x) "d"x`
The value of `int_0^(pi/2) log ((4 + 3 sin x)/(4 + 3 cos x)) dx` is
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.
Find: `int e^x.sin2xdx`
Find: `int (2x)/((x^2 + 1)(x^2 + 2)) dx`
Solve: `int sqrt(4x^2 + 5)dx`
`int(logx)^2dx` equals ______.
Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.
Evaluate :
`int(4x - 6)/(x^2 - 3x + 5)^(3/2) dx`
`int(1-x)^-2 dx` = ______
Evaluate the following.
`int x^3 e^(x^2) dx`
`int logx dx = x(1+logx)+c`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4))dx`
`int (sin^-1 sqrt(x) + cos^-1 sqrt(x))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 the following:
`intx^3e^(x^2)dx`
Evaluate `int (1 + x + x^2/(2!))dx`
Evaluate:
`int x^2 cos x dx`
