Advertisements
Advertisements
Question
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Advertisements
Solution
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
RELATED QUESTIONS
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Solve:
dy/dx = cos(x + y)
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Write a value of
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals: `int sin 4x cos 3x dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
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` =
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Evaluate `int 1/(x (x - 1))` dx
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Write `int cotx dx`.
Evaluate `int (1)/(x(x - 1))dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
