Advertisements
Advertisements
Question
`int 1/(x^2 - "a"^2) "d"x` = ______ + c
Advertisements
Solution
`1/(2"a") log |(x - "a")/(x + "a")|`
APPEARS IN
RELATED QUESTIONS
If `int_(-pi/2)^(pi/2)sin^4x/(sin^4x+cos^4x)dx`, then the value of I is:
(A) 0
(B) π
(C) π/2
(D) π/4
If u and v are two functions of x then prove that
`intuvdx=uintvdx-int[du/dxintvdx]dx`
Hence evaluate, `int xe^xdx`
Evaluate `int_0^(pi)e^2x.sin(pi/4+x)dx`
Integrate the function in x sin x.
Integrate the function in x sin 3x.
Integrate the function in x sin−1 x.
Integrate the function in `e^x (1/x - 1/x^2)`.
Evaluate the following : `int x^2tan^-1x.dx`
Integrate the following functions w.r.t. x : `(x + 1) sqrt(2x^2 + 3)`
Integrate the following functions w.r.t. x : [2 + cot x – cosec2x]ex
Choose the correct options from the given alternatives :
`int tan(sin^-1 x)*dx` =
Integrate the following with respect to the respective variable : `(sin^6θ + cos^6θ)/(sin^2θ*cos^2θ)`
Integrate the following w.r.t.x : `log (1 + cosx) - xtan(x/2)`
Evaluate the following.
`int x^2 e^4x`dx
Evaluate the following.
`int (log "x")/(1 + log "x")^2` dx
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
`int (sinx)/(1 + sin x) "d"x`
Choose the correct alternative:
`intx^(2)3^(x^3) "d"x` =
`int "e"^x x/(x + 1)^2 "d"x`
`int 1/sqrt(x^2 - a^2)dx` = ______.
`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.
If `int (f(x))/(log(sin x))dx` = log[log sin x] + c, then f(x) is equal to ______.
`int(3x^2)/sqrt(1+x^3) dx = sqrt(1+x^3)+c`
Evaluate `int(1 + x + (x^2)/(2!))dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)`dx
Evaluate the following.
`intx^3 e^(x^2)dx`
The value of `int (x sin^-1)/(sqrt(1 - x^2)) dx` is equal to:
