Advertisements
Advertisements
प्रश्न
`int cos^7 x "d"x`
Advertisements
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
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`e^(2x+3)`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
cot x log sin x
Write a value of
Write a value of
Write a value of
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Evaluate the following integrals:
`int x/(x + 2).dx`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).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 : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
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: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: `int log ("x"^2 + "x")` dx
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int cos sqrtx` dx = _____________
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int (cos2x)/(sin^2x) "d"x`
`int(log(logx))/x "d"x`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
After choosing \[u=g(x)\], what is the next step?
In \[\int\sin^3x\cos^2x\,dx\], which rewriting prepares the integrand for the substitution \[t=\cos x\]?
