Advertisements
Advertisements
प्रश्न
`int cos^7 x "d"x`
उत्तर
Let I = `int cos^7 x "d"x`
= `int(cos^2x)^3*cosx "d"x`
= `int (1 - sin^2x)^3* cosx "d"x`
Put sin x = t
∴ cos x dx = dt
∴ I = `int (1 - "t"^2)^3 "dt"`
= `int (1 - 3"t"^2 + 3"t"^4 - "t"^6) "dt"`
= `int 1* "dt" - 3 int "t"^2 "dt" + 3 int "t"^4 "dt" - int "t"^6 "dt"`
= `"t" - 3 ("t"^3/3) + 3"t"^5/5) - "t"^7/7 + "c"`
∴ I = `sinx - sin^3x + 3/5 sin^5x - 1/7 sin^7x + "c"`
संबंधित प्रश्न
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
`sin x/(1+ cos x)`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Evaluate: `int 1/(x(x-1)) dx`
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Write a value of
Write a value of
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\left( e^{x \log_e \text{ a}} + e^{a \log_e x} \right) dx\] .
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
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(5x + 2)/(3x - 4).dx`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Evaluate the following : `int sinx/(sin 3x).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Evaluate the following integrals : `int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate `int 1/("x" ("x" - 1))` dx
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate the following.
`int 1/(4"x"^2 - 20"x" + 17)` dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
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 1/(2"x" + 3"x" log"x")` dx
Evaluate: `int 1/(sqrt("x") + "x")` dx
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int x^x (1 + logx) "d"x`
`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`
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
If f'(x) = `x + 1/x`, then f(x) is ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
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`
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
Evaluate `int (1)/(x(x - 1))dx`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
`int "cosec"^4x dx` = ______.
Evaluate:
`int sin^2(x/2)dx`
Evaluate the following.
`int1/(x^2+4x-5) dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate `int1/(x(x-1))dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int 1/(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`
