Advertisements
Advertisements
प्रश्न
Evaluate the following.
`int 1/(4"x"^2 - 20"x" + 17)` dx
Evaluate:
`∫ 1/(4x^2 − 20x + 17) dx`
Advertisements
उत्तर
Let I = `int 1/(4"x"^2 - 20"x" + 17)` dx
= `1/4 int 1/("x"^2 - 5"x" + 17/4)` dx
= `1/4 int 1/("x"^2 - 2 * 5/2 "x" + 25/4 - 25/4 + 17/4)` dx
= `1/4 int 1/(("x" - 5/2)^2 - 8/4)` dx
= `1/4 int 1/(("x" - 5/2)^2 - (sqrt2)^2)` dx
= `1/4 xx 1/(2sqrt2) log |("x" - 5/2 - sqrt2)/("x" - 5/2 + sqrt2)|` + c
∴ I = `1/(8sqrt2) log |(2"x" - 5 - 2sqrt2)/(2"x" - 5 + 2sqrt2)|` + c
संबंधित प्रश्न
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals : tan2x dx
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Evaluate: `int "x" * "e"^"2x"` dx
If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate `int1/(x(x-1))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int(1+x+x^2/(2!))dx`
