Advertisements
Advertisements
प्रश्न
`int 1/sqrt(x^2 - 9) dx` = ______.
पर्याय
`1/3 log |x + sqrt(x^2 - 9)| + c`
`log |x + sqrt(x^2 - 9)| + c`
`3log |x + sqrt(x^2 - 9)| + c`
`log |x - sqrt(x^2 - 9)| + c`
उत्तर
`int 1/sqrt(x^2 - 9) dx` = `bb(log |x + sqrt(x^2 - 9)| + c)`.
Explanation:
`int 1/sqrt(x^2 - 9) dx = int 1/sqrt(x^2 - 3^2) dx`
= `log |x + sqrt(x^2 - 3^2)| + c`
= `log |x + sqrt(x^2 - 9)| + c`
APPEARS IN
संबंधित प्रश्न
`int1/xlogxdx=...............`
(A)log(log x)+ c
(B) 1/2 (logx )2+c
(C) 2log x + c
(D) log x + c
If u and v are two functions of x then prove that
`intuvdx=uintvdx-int[du/dxintvdx]dx`
Hence evaluate, `int xe^xdx`
Integrate the function in x log 2x.
Integrate the function in x tan-1 x.
Integrate the function in (sin-1x)2.
Integrate the function in `(xe^x)/(1+x)^2`.
Integrate the function in `((x- 3)e^x)/(x - 1)^3`.
Evaluate the following:
`int x.sin 2x. cos 5x.dx`
Integrate the following functions w.r.t. x : `e^(2x).sin3x`
Integrate the following functions w.r.t. x : `x^2 .sqrt(a^2 - x^6)`
Integrate the following functions w.r.t. x : cosec (log x)[1 – cot (log x)]
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Evaluate the following.
`int (log "x")/(1 + log "x")^2` dx
Evaluate: `int "e"^"x"/(4"e"^"2x" -1)` dx
`int (sin(x - "a"))/(cos (x + "b")) "d"x`
`int ("d"x)/(x - x^2)` = ______
Evaluate the following:
`int ((cos 5x + cos 4x))/(1 - 2 cos 3x) "d"x`
Find the general solution of the differential equation: `e^((dy)/(dx)) = x^2`.
`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.
Evaluate :
`int(4x - 6)/(x^2 - 3x + 5)^(3/2) dx`
Evaluate `int(1 + x + (x^2)/(2!))dx`
Evaluate:
`intcos^-1(sqrt(x))dx`
Evaluate:
`inte^x sinx 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 the following.
`int x^3 e^(x^2) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)`dx
Evaluate:
`inte^x "cosec" x(1 - cot x)dx`
Evaluate the following.
`intx^3 e^(x^2)dx`
Evaluate `int(1 + x + x^2/(2!))dx`.
Evaluate the following.
`intx^3/(sqrt(1 + x^4))dx`
