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
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`xsqrt(x + 2)`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
sec2(7 – 4x)
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
`int sqrt(1 + "x"^2) "dx"` =
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
`int x^2/sqrt(1 - x^6)` dx = ________________
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
`int(log(logx))/x "d"x`
`int x^3"e"^(x^2) "d"x`
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.
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(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
Evaluate `int1/(x(x - 1))dx`
