Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : cos7x
Advertisements
उत्तर
Let I = `int cos^7x dx`
= `int cos^6x.cos x dx`
= `int (1 - sin^2x)^3 cos x dx`
Put, sin x = t
∴ cos x dx = dt
I = `int(1 - t^2)^3 dt`
= `int(1 - 3t^2 + 3t^4 - t^6)dt`
= `int 1dt - 3 int t^2dt + 3intt^4 dt - int t^6 dt`
= `t - 3(t^3/3) + 3(t^5/3) - t^7/(7) + c`
= `sinx - sin^3x + (3)/(5)sin^5x - (1)/(7)sin^7x + c`.
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Integrate the functions:
cot x log sin x
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Evaluate: `int (sec x)/(1 + cosec x) dx`
Write a value of
Write a value of
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following:
`int sinx/(sin 3x) 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 - 2cos 2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
`int logx/(log ex)^2*dx` = ______.
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
Evaluate the following.
`int 1/(4x^2 - 20x + 17)` dx
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
`int logx/x "d"x`
`int(1 - x)^(-2) dx` = ______.
`int dx/(1 + e^-x)` = ______
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int(log(logx) + 1/(logx)^2)dx` = ______.
`int cos^3x dx` = ______.
`int (logx)^2/x dx` = ______.
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
`int secx/(secx - tanx)dx` equals ______.
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int 1/(x(x-1)) dx`
