Advertisements
Advertisements
Question
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Advertisements
Solution
Let `I = int (4x + 2) sqrt(x^2 + x + 1)` dx
or `I = 2 int (2x + 1) sqrt ((x^2 + x + 1))` dx
Taking x2 + x + 1 = t
2x + 1 = dt
Hence, `I = 2 int sqrt t dt`
`= 2 int t^(1/2) dt = 2. 2/3 t^(3/2) + C`
`= 4/3 (x^2 + x + 1)^(3/2) + C`
APPEARS IN
RELATED QUESTIONS
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Integrate the functions:
`xsqrt(x + 2)`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
`int (dx)/(sin^2 x cos^2 x)` equals:
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Write a value of
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
`int "dx"/(9"x"^2 + 1)= ______. `
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals:
`int x/(x + 2).dx`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Evaluate `int (3"x"^2 - 5)^2` dx
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
`int sqrt(1 + sin2x) dx`
`int logx/x "d"x`
`int (1 + x)/(x + "e"^(-x)) "d"x`
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.
Evaluate `int(1+ x + x^2/(2!)) dx`
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
