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
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Solve:
dy/dx = cos(x + y)
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
The value of \[\int\frac{1}{x + x \log x} dx\] is
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Integrate the following w.r.t. x : x3 + x2 – x + 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)`
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Evaluate `int (1 + x + x^2/(2!))`dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.
`int 1/(sinx.cos^2x)dx` = ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
`int cos^3x dx` = ______.
Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.
Evaluate `int (1)/(x(x - 1))dx`
`int x^2/sqrt(1 - x^6)dx` = ______.
Evaluate the following.
`int x^3 e^(x^2) 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).
`int (x + 1)/(x(1 + xe^x)) dx` is equal to
