Advertisements
Advertisements
Question
Integrate the functions:
`xsqrt(1+ 2x^2)`
Advertisements
Solution
Let `I = int x sqrt(1 + 2x^2)` dx
Taking 1 + 2x2 = t
4x dx = dt
or x dx `= 1/4` dt
Hence, `I = int 1/4 t^(1/2) dt = 1/4 int t^(1/2)` dt
`= 1/4 . 2/3 t^(3/2) + C`
`= 1/6 (1 + 2x^2)^(3/2) + C`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Find `intsqrtx/sqrt(a^3-x^3)dx`
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`e^(2x+3)`
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals:
`int x/(x + 2).dx`
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Evaluate the following.
`int 1/("x" log "x")`dx
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.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int cot^2x "d"x`
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
Write `int cotx dx`.
`int x^3 e^(x^2) dx`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
`int "cosec"^4x dx` = ______.
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
