Advertisements
Advertisements
प्रश्न
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
Advertisements
उत्तर
Let I = `int 1/(sqrt("x"^2 -8"x" - 20))` dx
`= int 1/(sqrt ("x"^2 - 2 * 4"x" + 16 - 16 - 20))` dx
`= int "dx"/sqrt(("x - 4")^2 - 36)` dx
`= int "dx"/(sqrt(("x - 4")^2 - 6^2))` dx
`= log |("x - 4") + sqrt(("x - 4")^2 - 6^2)|` + c
∴ I = `log |("x - 4") + sqrt("x"^2 - 8"x" - 20)|` + c
Notes
The answer in the textbook is incorrect.
APPEARS IN
संबंधित प्रश्न
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Find: `int(x+3)sqrt(3-4x-x^2dx)`
Integrate the functions:
`xsqrt(x + 2)`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t.x:
cos8xcotx
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate: `int 1/(sqrt("x") + "x")` dx
Evaluate: `int log ("x"^2 + "x")` dx
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int cos^7 x "d"x`
`int(log(logx))/x "d"x`
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
`int ("d"x)/(x(x^4 + 1))` = ______.
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
`int cos^3x dx` = ______.
`int secx/(secx - tanx)dx` equals ______.
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
