Advertisements
Advertisements
प्रश्न
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
विकल्प
`e^x/x + c`
`e^x/x^2 + c`
`(x - 1/x)e^x + c`
`xe^-x + c`
Advertisements
उत्तर
`e^x/x + c`
APPEARS IN
संबंधित प्रश्न
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Write a value of
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int cot^2x "d"x`
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "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"`
Evaluate `int(3x^2 - 5)^2 "d"x`
`int sin^-1 x`dx = ?
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
Write `int cotx dx`.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate `int1/(x(x-1))dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
If \[x=g(t)\] and \[dx=g'(t)dt\], which formula represents integration by substitution?
Which substitution is appropriate for \[\sqrt{\frac{x}{a-x}}\], \[\sqrt{\frac{a-x}{x}}\], \[\sqrt{x(a-x)}\], or \[\frac{1}{\sqrt{x(a-x)}}\]?
For \[\sqrt{\frac{x-\alpha}{\beta-x}}\] or \[\sqrt{(x-\alpha)(\beta-x)}\], where \[\beta>\alpha\], which substitution is used?
