Advertisements
Advertisements
प्रश्न
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
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
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Find : `int(x+3)sqrt(3-4x-x^2dx)`
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`xsqrt(x + 2)`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Integrate the functions:
`1/(1 - tan x)`
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of
Write a value of
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
`int "dx"/(9"x"^2 + 1)= ______. `
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
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:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).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)/(2sin 2x - 3)dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3)dx`
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
Fill in the Blank.
To find the value of `int ((1 + log "x") "dx")/"x"` the proper substitution is ________
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 (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate: `int "x" * "e"^"2x"` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int 1/(xsin^2(logx)) "d"x`
`int x/(x + 2) "d"x`
Choose the correct alternative:
`int(1 - x)^(-2) dx` = ______.
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
`int(5x + 2)/(3x - 4) dx` = ______
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int (cos x)/(1 - sin x) "dx" =` ______.
`int ("d"x)/(x(x^4 + 1))` = ______.
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
`int (logx)^2/x dx` = ______.
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate:
`int(cos 2x)/sinx dx`
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate `int1/(x(x-1))dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
Evaluate `int (1 + x + x^2/(2!)) 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).
