Advertisements
Advertisements
Question
Integrate the functions:
`x/(9 - 4x^2)`
Advertisements
Solution
Let `I = int x/(9 - 4x^2)` dx
Put 9 - 4x2 = t
⇒ -8x dx = dt
∴ `I = -1/8 int dt/t`
`= -1/8 log |t| + C`
`= 1/8 log 1/ |t| + C`
`= 1/8 log 1/ (|9 - 4x^2|) +C`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Integrate the functions:
`1/(1 - tan x)`
Integrate the functions:
`(1+ log x)^2/x`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Write a value of
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals : `int cos^2x.dx`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int (cos2x)/(sin^2x) "d"x`
`int cos^7 x "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
`int1/(4 + 3cos^2x)dx` = ______
`int sec^6 x tan x "d"x` = ______.
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate `int (1)/(x(x - 1))dx`
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
