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
Prove that: `int sqrt(a^2 - x^2) * dx = x/2 * sqrt(a^2 - x^2) + a^2/2 * sin^-1(x/a) + c`
Integrate the function in x sin x.
Integrate the function in `x^2e^x`.
Integrate the function in x2 log x.
Integrate the function in x (log x)2.
Integrate the function in e2x sin x.
Prove that:
`int sqrt(x^2 + a^2)dx = x/2 sqrt(x^2 + a^2) + a^2/2 log |x + sqrt(x^2 + a^2)| + c`
Evaluate the following : `int x^3.logx.dx`
Integrate the following functions w.r.t. x : `sqrt(4^x(4^x + 4))`
Integrate the following functions w.r.t. x : `sec^2x.sqrt(tan^2x + tan x - 7)`
Integrate the following functions w.r.t. x : `e^(sin^-1x)*[(x + sqrt(1 - x^2))/sqrt(1 - x^2)]`
Choose the correct options from the given alternatives :
`int tan(sin^-1 x)*dx` =
Evaluate the following.
`int "e"^"x" "x - 1"/("x + 1")^3` dx
Evaluate: `int "dx"/(3 - 2"x" - "x"^2)`
Evaluate: `int "dx"/("x"[(log "x")^2 + 4 log "x" - 1])`
Evaluate `int 1/(x(x - 1)) "d"x`
`int "e"^x x/(x + 1)^2 "d"x`
`int [(log x - 1)/(1 + (log x)^2)]^2`dx = ?
`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.
`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.
Find: `int e^x.sin2xdx`
Find the general solution of the differential equation: `e^((dy)/(dx)) = x^2`.
`intsqrt(1+x) dx` = ______
Evaluate `int(3x-2)/((x+1)^2(x+3)) dx`
Evaluate:
`int e^(logcosx)dx`
Evaluate:
`int (sin(x - a))/(sin(x + a))dx`
Complete the following activity:
`int_0^2 dx/(4 + x - x^2) `
= `int_0^2 dx/(-x^2 + square + square)`
= `int_0^2 dx/(-x^2 + x + 1/4 - square + 4)`
= `int_0^2 dx/ ((x- 1/2)^2 - (square)^2)`
= `1/sqrt17 log((20 + 4sqrt17)/(20 - 4sqrt17))`
Evaluate `int (1 + x + x^2/(2!))dx`
`∫ sin^(−1)` xdx is equal to ______.
