Advertisements
Advertisements
प्रश्न
`int 1/(4x^2 - 20x + 17) "d"x`
Advertisements
उत्तर
Let I = `int 1/(4x^2 - 20x + 17) "d"x`
= `int 1/(4(x^2 - 5x + 17/4)) "d"x`
`(1/2 "coefficient of" x)^2 = (1/2 xx (-5))^2`
= `25/4`
∴ I = `1/4 int 1/(x^2 - 5x + 25/4 - 25/4 + 17/4) "d"x`
= `1/4 int 1/((x - 5/2)^2 - 2) "d"x`
= `1/4 int 1/((x - 5/2)^2 - (sqrt(2))^2) "d"x`
= `1/4 * 1/(2sqrt(2)) log |(x - 5/2 - sqrt(2))/(x - 5/2 + sqrt(2))| + "c"`
∴ I = `1/(8sqrt(2)) log|(2x - 5 - 2sqrt(2))/(2x - 5 + 2sqrt(2))| + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int x^2/((x^2+2)(2x^2+1))dx`
Integrate the rational function:
`1/(x^2 - 9)`
Integrate the rational function:
`x/((x^2+1)(x - 1))`
Integrate the rational function:
`1/(x^4 - 1)`
Integrate the rational function:
`((x^2 +1)(x^2 + 2))/((x^2 + 3)(x^2+ 4))`
`int (dx)/(x(x^2 + 1))` equals:
Find `int (2cos x)/((1-sinx)(1+sin^2 x)) dx`
Integrate the following w.r.t. x : `x^2/((x^2 + 1)(x^2 - 2)(x^2 + 3))`
Integrate the following w.r.t. x : `(12x^2 - 2x - 9)/((4x^2 - 1)(x + 3)`
Integrate the following w.r.t. x : `(1)/(x(x^5 + 1)`
Integrate the following w.r.t. x : `(5x^2 + 20x + 6)/(x^3 + 2x ^2 + x)`
Integrate the following w.r.t. x : `(1)/(x^3 - 1)`
Integrate the following w.r.t. x : `(1)/(sin2x + cosx)`
Choose the correct options from the given alternatives :
If `int tan^3x*sec^3x*dx = (1/m)sec^mx - (1/n)sec^n x + c, "then" (m, n)` =
Integrate the following w.r.t. x: `(2x^2 - 1)/(x^4 + 9x^2 + 20)`
Integrate the following with respect to the respective variable : `(cos 7x - cos8x)/(1 + 2 cos 5x)`
Integrate the following w.r.t.x : `(1)/((1 - cos4x)(3 - cot2x)`
Evaluate: `int (2"x" + 1)/(("x + 1")("x - 2"))` dx
Evaluate: `int 1/("x"("x"^5 + 1))` dx
Evaluate: `int (5"x"^2 + 20"x" + 6)/("x"^3 + 2"x"^2 + "x")` dx
For `int ("x - 1")/("x + 1")^3 "e"^"x" "dx" = "e"^"x"` f(x) + c, f(x) = (x + 1)2.
Evaluate: `int ("3x" - 1)/("2x"^2 - "x" - 1)` dx
Evaluate: `int (2"x"^3 - 3"x"^2 - 9"x" + 1)/("2x"^2 - "x" - 10)` dx
`int x^2sqrt("a"^2 - x^6) "d"x`
`int 1/(x(x^3 - 1)) "d"x`
If f'(x) = `x - 3/x^3`, f(1) = `11/2` find f(x)
`int sin(logx) "d"x`
`int "e"^(sin^(-1_x))[(x + sqrt(1 - x^2))/sqrt(1 - x^2)] "d"x`
`int "e"^x ((1 + x^2))/(1 + x)^2 "d"x`
`int (3x + 4)/sqrt(2x^2 + 2x + 1) "d"x`
`int x^3tan^(-1)x "d"x`
`int x sin2x cos5x "d"x`
`int xcos^3x "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 "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.
Find: `int x^2/((x^2 + 1)(3x^2 + 4))dx`
`int 1/(x^2 + 1)^2 dx` = ______.
Find: `int x^4/((x - 1)(x^2 + 1))dx`.
Find : `int (2x^2 + 3)/(x^2(x^2 + 9))dx; x ≠ 0`.
Evaluate`int(5x^2-6x+3)/(2x-3)dx`
Evaluate.
`int (5x^2 - 6x + 3) / (2x -3) dx`
Evaluate:
`int(2x^3 - 1)/(x^4 + x)dx`
