Advertisements
Advertisements
Question
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Advertisements
Solution
`int (1)/sqrt(x^2 + 8x - 20).dx`
= `int (1)/(sqrt((x^2 + 8x + 16) - 16 - 20)).dx`
= `int (1)/(sqrt((x + 4)^2 - 36)).dx`
= `int (1)/(sqrt((x + 4)^2 - (6)^2)).dx`
= `log|(x + 4) + sqrt((x + 4)^2 - (6)^2)| + c`
= `log|(x + 4) + sqrt(x^2 + 8x - 20)| + c`.
APPEARS IN
RELATED QUESTIONS
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Write a value of
Write a value of
Write a value of
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following:
`int sinx/(sin 3x) dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Evaluate the following : `int (logx)2.dx`
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int 1/("x" log "x")`dx
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: `int "e"^sqrt"x"` dx
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int (sin4x)/(cos 2x) "d"x`
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int cot^2x "d"x`
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int (cos x)/(1 - sin x) "dx" =` ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate:
`int sin^3x cos^3x dx`
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate `int1/(x(x - 1))dx`
Evaluate `int 1/(x(x-1)) dx`
Evaluate:
`intsqrt(sec x/2 - 1)dx`
