Advertisements
Advertisements
Question
`int "dx"/(9"x"^2 + 1)= ______. `
Options
`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
Solution
`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
RELATED QUESTIONS
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Write a value of
Write a value of
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Integrate the following w.r.t. x : x3 + x2 – x + 1
Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
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 (cos2x)/(sin^2x) "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate:
`int sin^3x cos^3x dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
