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
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Integrate the functions:
`1/(1 - tan x)`
Write a value of
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
Evaluate the following integrals : `int cos^2x.dx`
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 : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
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 : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).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 the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` 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 = ?
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
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
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
Evaluate: `int 1/(sqrt("x") + "x")` dx
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int(log(logx))/x "d"x`
`int(1 - x)^(-2) dx` = ______.
State whether the following statement is True or False:
If `int x "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate `int1/(x(x - 1))dx`
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
