Advertisements
Advertisements
प्रश्न
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Advertisements
उत्तर
Let I = `int 1/("a"^2 - "b"^2 "x"^2)` dx
`= 1/"b"^2 int 1/("a"^2/"b"^2 - "x"^2)`dx
`= 1/"b"^2 int 1/(("a"/"b")^2 - "x"^2)` dx
`= 1/"b"^2 xx 1/(2("a"/"b")) log |("a"/"b" + "x")/("a"/"b" - "x")|` + c
∴ I = `1/"2ab" log |("a" + "bx")/("a" - "bx")|` + c
Alternate Method:
Let I = `int "dx"/("a"^2 - "b"^2"x"^2) = int"dx"/("a"^2 - ("bx")^2)`
`= 1/(2 xx "a") xx 1/"b" log |("a" + "bx")/("a" - "bx")|` + c
∴ I = `1/"2ab" log |("a" + "bx")/("a" - "bx")|` + c
Notes
The answer in the textbook is incorrect.
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`xsqrt(1+ 2x^2)`
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Integrate the following functions w.r.t. x : cos7x
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate: `int "e"^sqrt"x"` dx
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
State whether the following statement is True or False:
If `int x "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`
Evaluate `int(3x^2 - 5)^2 "d"x`
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
`int (cos x)/(1 - sin x) "dx" =` ______.
`int cos^3x dx` = ______.
`int (logx)^2/x dx` = ______.
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluate the following
`int1/(x^2 +4x-5)dx`
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
