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
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Integrate the functions:
cot x log sin x
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Evaluate the following:
`int sinx/(sin 3x) dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Evaluate the following : `int (logx)2.dx`
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
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).
Evaluate: `int "x" * "e"^"2x"` dx
`int (sin4x)/(cos 2x) "d"x`
`int ("d"x)/(x(x^4 + 1))` = ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
`int secx/(secx - tanx)dx` equals ______.
Evaluate the following
`int1/(x^2 +4x-5)dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
