Advertisements
Advertisements
Question
Integrate the functions:
`xsqrt(x + 2)`
Advertisements
Solution
Let `I = int x sqrt(x + 2)` dx
Taking `sqrt(x + 2) = t`
or x + 2 = t2
or dx = 2t dt
Hence, `I = int (t^2 - 2). t. 2t dt`
`= int 2t^4 - 4t^2 dt`
`= 2 int (t^4 - 2t^2)` dt
`= 2 int t^4 dt - 4 int` t2 dt
`= 2/5 t^5 - 4/3 t^3 + C`
`=> 2/5 (x + 2)^(5/2) - 4/3 (x + 2)^(3/2) + C`
APPEARS IN
RELATED QUESTIONS
Find `intsqrtx/sqrt(a^3-x^3)dx`
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`(log x)^2/x`
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Write a value of
Write a value of
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Evaluate the following integrals : tan2x dx
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t. x : tan5x
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Evaluate the following : `int (logx)2.dx`
Evaluate `int 1/("x" ("x" - 1))` dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Evaluate `int "x - 1"/sqrt("x + 4")` dx
Evaluate: ∫ |x| dx if x < 0
Evaluate: `int log ("x"^2 + "x")` dx
`int (log x)/(log ex)^2` dx = _________
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int x^x (1 + logx) "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int dx/(1 + e^-x)` = ______
`int cos^3x dx` = ______.
Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.
Evaluate the following
`int1/(x^2 +4x-5)dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
