Advertisements
Advertisements
प्रश्न
`int "dx"/(9"x"^2 + 1)= ______. `
पर्याय
`1/3 "tan"^-1(2"x") +"c"`
`1/3 "tan"^-1"x" +"c"`
`1/3 "tan"^-1(3"x") +"c"`
`1/3 "tan"^-1(6"x") +"c"`
Advertisements
उत्तर
`1/3 "tan"^-1(3"x") +"c"`
Let I = `int "dx"/(9"x"^2 + 1)`
= `1/9 int "dx"/(("x"^2) +(1/3)^2)`
= `1/9 1/(1/3) "tan"^-1("x"/(1/3)) + "C"`
`= 1/3 "tan"^-1(3"x") + "c"`
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
`xsqrt(x + 2)`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
cot x log sin x
Write a value of
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
`int sqrt(1 + "x"^2) "dx"` =
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
Fill in the Blank.
`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int 1/(xsin^2(logx)) "d"x`
`int(1 - x)^(-2) dx` = ______.
`int (7x + 9)^13 "d"x` ______ + c
State whether the following statement is True or False:
If `int x "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
If f'(x) = 4x3- 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate `int1/(x(x - 1))dx`
`int (x + 1)/(x(1 + xe^x)) dx` is equal to
