Advertisements
Advertisements
Questions
Evaluate the following.
`int 1/(4x^2 - 20x + 17)` dx
Evaluate:
`∫ 1/(4x^2 − 20x + 17) dx`
Advertisements
Solution
Let I = `int 1/(4x^2 - 20x + 17)` dx
= `1/4 int 1/(x^2 - 5x + 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 |(2x - 5 - 2sqrt2)/(2x - 5 + 2sqrt2)|` + c
RELATED QUESTIONS
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`1/(1 - tan x)`
Write a value of
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
The value of \[\int\frac{1}{x + x \log x} dx\] is
Evaluate the following integrals:
tan2x dx
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Evaluate `int (1 + x + x^2/(2!))`dx
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int sqrt(1 + sin2x) dx`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int cot^2x "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
State whether the following statement is True or False:
If `int x "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
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 (logx)^2/x dx` = ______.
Evaluate `int(1+x+x^2/(2!))dx`
In \[\int\sin^3x\cos^2x\,dx\], which rewriting prepares the integrand for the substitution \[t=\cos x\]?
