Advertisements
Advertisements
प्रश्न
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Advertisements
उत्तर
`int (2x - 7)/sqrt(4x - 1).dx`
= `(1)/(2)int(2(2x - 7))/sqrt(4x - 1).dx`
= `(1)/(2)int((4x - 1) - 13)/sqrt(4x - 1).dx`
= `(1)/(2)int(((4x - 1))/sqrt(4x - 1) - 13/sqrt(4x - 1)).dx`
= `(1)/(2)int (4x - 1)^(1/2).dx - 13/2 int(4x - 1)^(-1/2).dx`
= `(1)/(2)((4x - 1)^(3/2))/((4)(3/2)) - (13)/(2).((4x - 1)^(1/2))/((4)(1/2)) + c`
= `(1)/(12)(4x - 1)^(3/2) - (13)/(4)sqrt(4x - 1) + c`
संबंधित प्रश्न
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
cot x log sin x
Integrate the functions:
`1/(1 - tan x)`
Solve:
dy/dx = cos(x + y)
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
The value of \[\int\frac{1}{x + x \log x} dx\] is
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x : sin4x.cos3x
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 : `int (1)/sqrt(11 - 4x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
`int x^2/sqrt(1 - x^6)` dx = ________________
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int 1/(xsin^2(logx)) "d"x`
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
`int (1 + x)/(x + "e"^(-x)) "d"x`
`int dx/(1 + e^-x)` = ______
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate `int(1+ x + x^2/(2!)) dx`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate `int 1/(x(x-1))dx`
If f'(x) = 4x3- 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate:
`int sin^3x cos^3x dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate:
`intsqrt(sec x/2 - 1)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
