Advertisements
Advertisements
प्रश्न
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
पर्याय
`(1)/(2)sqrt(x + 1) + c`
`(2)/(3)(x + 1)^(3/2) + c`
`sqrt(x + 1) + c`
`2(x - 1)^(3/2) + c`
उत्तर
`(2)/(3)(x + 1)^(3/2) + c`
Explanation:
`I = int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx`
I = `int sqrt((1+x)^2+ sqrtx *sqrt(1+ x) )/ (sqrt(x) + sqrt(1+x))*dx`
I = `int( sqrt(1 + x) sqrt(1 + x) + sqrtx )/ (sqrt(x)+sqrt(1 + x))*dx`
I `= int(sqrt(1+x)) dx = 2/3 (x + 1)^(3/2) + c`
I = `(2)/(3)(x + 1)^(3/2) + c`
APPEARS IN
संबंधित प्रश्न
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
sec2(7 – 4x)
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Integrate the functions:
`sin x/(1+ cos x)`
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
The value of \[\int\frac{1}{x + x \log x} dx\] is
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Evaluate the following integrals : `int(x - 2)/sqrt(x + 5).dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
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)/(cos2x + 3sin^2x).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)/(3 + 2 sin2x + 4cos 2x).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
Evaluate the following : `int (logx)2.dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
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` + ______
Evaluate: ∫ |x| dx if x < 0
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int sqrt(1 + sin2x) "d"x`
`int x/(x + 2) "d"x`
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
`int x^3"e"^(x^2) "d"x`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int (cos x)/(1 - sin x) "dx" =` ______.
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
If f'(x) = `x + 1/x`, then f(x) 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(log(logx) + 1/(logx)^2)dx` = ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
`int (logx)^2/x dx` = ______.
`int secx/(secx - tanx)dx` equals ______.
Evaluate `int(1 + x + x^2/(2!))dx`
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
`int x^3 e^(x^2) 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).
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate `int(1+x+(x^2)/(2!))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
Evaluate `int 1/(x(x-1))dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
