Advertisements
Advertisements
प्रश्न
`int sec^2x sqrt(tan^2x + tanx - 7) "d"x`
Advertisements
उत्तर
Let I = `int sec^2x sqrt(tan^2x + tanx - 7) "d"x`
Put tan x = t
∴ sec2x dx = dt
∴ I = `int sqrt("t"^2 + "t" - 7) "dt"`
= `int sqrt("t"^2 + "t" + 1/4- 1/4 - 7) "dt"`
= `intsqrt(("t" + 1/2)^2 - 29/4) "dt"`
= `int sqrt(("t" +1/2)^2 - ((sqrt(29))/2)^2) "dt"`
= `("t" + 1/2)/2 sqrt(("t" + 1/2)^2 - (sqrt(29)/2)^2`
= `- (sqrt(29)/2)^2/2 log|"t" + 1/2 + sqrt("t"^2 + "t" -7)| + "c"`
= `(2"t" + 1)/4 sqrt("t"^2 + "t" - 7) - 29/8 log|"t" + 1/2 + sqrt("t"^2 + "t" - 7)| + "c"`
∴ I = `((2tan x + 1))/4 sqrt(tan^2 x + tanx - 7) - 29/8 log|tanx + 1/2 + sqrt(tan^2x + tanx - 7)| + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int x^2/((x^2+2)(2x^2+1))dx`
Find : `int x^2/(x^4+x^2-2) dx`
Evaluate:
`int x^2/(x^4+x^2-2)dx`
Integrate the rational function:
`1/(x^2 - 9)`
Integrate the rational function:
`x/((x-1)(x- 2)(x - 3))`
Integrate the rational function:
`x/((x^2+1)(x - 1))`
Integrate the rational function:
`((x^2 +1)(x^2 + 2))/((x^2 + 3)(x^2+ 4))`
Integrate the rational function:
`(2x)/((x^2 + 1)(x^2 + 3))`
Integrate the rational function:
`1/(e^x -1)`[Hint: Put ex = t]
Integrate the following w.r.t. x : `(x^2 + 2)/((x - 1)(x + 2)(x + 3)`
Integrate the following w.r.t. x : `(12x + 3)/(6x^2 + 13x - 63)`
Integrate the following w.r.t. x : `(2x)/(4 - 3x - x^2)`
Integrate the following w.r.t. x : `(x^2 + x - 1)/(x^2 + x - 6)`
Integrate the following w.r.t. x:
`(6x^3 + 5x^2 - 7)/(3x^2 - 2x - 1)`
Integrate the following w.r.t. x: `(1)/(sinx + sin2x)`
Integrate the following w.r.t. x : `(5*e^x)/((e^x + 1)(e^(2x) + 9)`
Integrate the following w.r.t. x: `(2x^2 - 1)/(x^4 + 9x^2 + 20)`
Integrate the following w.r.t.x : `(1)/(2cosx + 3sinx)`
Integrate the following w.r.t.x:
`x^2/((x - 1)(3x - 1)(3x - 2)`
Integrate the following w.r.t.x : `sec^2x sqrt(7 + 2 tan x - tan^2 x)`
Integrate the following w.r.t.x: `(x + 5)/(x^3 + 3x^2 - x - 3)`
Evaluate: `int "3x - 2"/(("x + 1")^2("x + 3"))` dx
Evaluate: `int 1/("x"("x"^"n" + 1))` dx
Evaluate: `int (1 + log "x")/("x"(3 + log "x")(2 + 3 log "x"))` dx
`int (7 + 4x + 5x^2)/(2x + 3)^(3/2) dx`
`int sqrt((9 + x)/(9 - x)) "d"x`
`int sec^3x "d"x`
`int (3x + 4)/sqrt(2x^2 + 2x + 1) "d"x`
`int x^3tan^(-1)x "d"x`
`int (x + sinx)/(1 - cosx) "d"x`
`int x^2/((x^2 + 1)(x^2 - 2)(x^2 + 3)) "d"x`
Choose the correct alternative:
`int sqrt(1 + x) "d"x` =
Choose the correct alternative:
`int ((x^3 + 3x^2 + 3x + 1))/(x + 1)^5 "d"x` =
`int 1/x^3 [log x^x]^2 "d"x` = p(log x)3 + c Then p = ______
Evaluate `int (2"e"^x + 5)/(2"e"^x + 1) "d"x`
`int x/((x - 1)^2 (x + 2)) "d"x`
If `intsqrt((x - 7)/(x - 9)) dx = Asqrt(x^2 - 16x + 63) + log|x - 8 + sqrt(x^2 - 16x + 63)| + c`, then A = ______
Evaluate the following:
`int (x^2"d"x)/(x^4 - x^2 - 12)`
Evaluate the following:
`int sqrt(tanx) "d"x` (Hint: Put tanx = t2)
`int 1/(x^2 + 1)^2 dx` = ______.
Evaluate:
`int 2/((1 - x)(1 + x^2))dx`
Evaluate:
`int (x + 7)/(x^2 + 4x + 7)dx`
Evaluate:
`int(2x^3 - 1)/(x^4 + x)dx`
