Advertisements
Advertisements
Question
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Advertisements
Solution
I = `int1/sqrt(3x^2 + 5x + 7)dx`
I = `1/sqrt3 int 1/sqrt(x^2 + (5x)/3 + 7/3)dx`
I = `1/sqrt3 int 1/sqrt((x^2 + (5x)/3 + 25/36) + (7/3 - 25/36))dx`
I = `1/sqrt3 int 1/sqrt((x^2 + (5x)/3 + (5/6)^2) + (59/36)).dx`
I = `1/sqrt3 int 1/sqrt((x + 5/6)^2 + (sqrt59/6)^2)dx`
I = `1/sqrt3 log |(x + 5/6) +sqrt((x + 5/2)^2 + (sqrt59/6)^2)| + c` ....`int1/sqrt(x^2 + a^2)dx = log|x + sqrt(x^2 + a^2)| + c`
I = `1/sqrt3 . log|(x + 5/6) + sqrt(x^2 + (5x)/3 + 7/3)| + c`
APPEARS IN
RELATED QUESTIONS
Find: `int(x+3)sqrt(3-4x-x^2dx)`
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
sec2(7 – 4x)
Evaluate: `int 1/(x(x-1)) dx`
Write a value of
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
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Evaluate the following : `int (logx)2.dx`
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
Evaluate: `int 1/(sqrt("x") + "x")` dx
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int (log x)/(log ex)^2` dx = _________
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
Evaluate `int(3x^2 - 5)^2 "d"x`
`int sin^-1 x`dx = ?
`int sec^6 x tan x "d"x` = ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
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(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
`int 1/(sinx.cos^2x)dx` = ______.
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
