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`
Find: `I=intdx/(sinx+sin2x)`
Integrate the rational function:
`(3x - 1)/((x - 1)(x - 2)(x - 3))`
Integrate the rational function:
`x/((x -1)^2 (x+ 2))`
Integrate the rational function:
`(3x + 5)/(x^3 - x^2 - x + 1)`
Integrate the rational function:
`(2x - 3)/((x^2 -1)(2x + 3))`
Integrate the rational function:
`(5x)/((x + 1)(x^2 - 4))`
Integrate the rational function:
`1/(x^4 - 1)`
Integrate the rational function:
`1/(x(x^n + 1))` [Hint: multiply numerator and denominator by xn − 1 and put xn = t]
Integrate the rational function:
`1/(x(x^4 - 1))`
Integrate the rational function:
`1/(e^x -1)`[Hint: Put ex = t]
Find `int (2cos x)/((1-sinx)(1+sin^2 x)) dx`
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 : `(12x^2 - 2x - 9)/((4x^2 - 1)(x + 3)`
Integrate the following w.r.t. x : `(2x)/((2 + x^2)(3 + x^2)`
Integrate the following w.r.t. x : `(3x - 2)/((x + 1)^2(x + 3)`
Integrate the following w.r.t. x : `((3sin - 2)*cosx)/(5 - 4sin x - cos^2x)`
Integrate the following w.r.t. x : `(1)/(sinx*(3 + 2cosx)`
Integrate the following with respect to the respective variable : `(6x + 5)^(3/2)`
Integrate the following w.r.t.x : `(1)/(sinx + sin2x)`
Evaluate:
`int x/((x - 1)^2(x + 2)) dx`
`int "dx"/(("x" - 8)("x" + 7))`=
Evaluate: `int (1 + log "x")/("x"(3 + log "x")(2 + 3 log "x"))` dx
`int x^2sqrt("a"^2 - x^6) "d"x`
`int 1/(x(x^3 - 1)) "d"x`
`int (7 + 4x + 5x^2)/(2x + 3)^(3/2) dx`
`int 1/(4x^2 - 20x + 17) "d"x`
`int "e"^x ((1 + x^2))/(1 + x)^2 "d"x`
`int x sin2x cos5x "d"x`
`int xcos^3x "d"x`
`int (3"e"^(2x) + 5)/(4"e"^(2x) - 5) "d"x`
Choose the correct alternative:
`int sqrt(1 + x) "d"x` =
`int (5(x^6 + 1))/(x^2 + 1) "d"x` = x5 – ______ x3 + 5x + c
`int x/((x - 1)^2 (x + 2)) "d"x`
Evaluate the following:
`int (x^2"d"x)/(x^4 - x^2 - 12)`
Evaluate the following:
`int (x^2 "d"x)/((x^2 + "a"^2)(x^2 + "b"^2))`
Evaluate the following:
`int (2x - 1)/((x - 1)(x + 2)(x - 3)) "d"x`
Evaluate the following:
`int "e"^(-3x) cos^3x "d"x`
The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, the denominator becomes eight times the numerator. Find the fraction.
If `intsqrt((x - 5)/(x - 7))dx = Asqrt(x^2 - 12x + 35) + log|x| - 6 + sqrt(x^2 - 12x + 35) + C|`, then A = ______.
Find : `int (2x^2 + 3)/(x^2(x^2 + 9))dx; x ≠ 0`.
Evaluate`int(5x^2-6x+3)/(2x-3)dx`
Evaluate:
`int 2/((1 - x)(1 + x^2))dx`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3)dx`
