Advertisements
Advertisements
Question
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Advertisements
Solution
Let I = `int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
`= int 1/sqrt("x"^2 + 2 * 2"x" + 4 - 4 + 29)` dx
`= int 1/(sqrt(("x + 2")^2 + 25)` dx
`= int "dx"/(sqrt(("x + 2")^2 + 5^2)`
`= log |("x + 2") + sqrt(("x + 2")^2 + 5^2)|`+ c
∴ I = `= log |("x + 2") + sqrt("x"^2 + "4x" + 29)|` + c
Notes
The answer in the textbook is incorrect.
APPEARS IN
RELATED QUESTIONS
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`sin x/(1+ cos x)`
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Write a value of\[\int \log_e x\ dx\].
The value of \[\int\frac{1}{x + x \log x} dx\] is
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
`int (log x)/(log ex)^2` dx = _________
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int logx/x "d"x`
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate `int1/(x(x - 1))dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
