Advertisements
Advertisements
प्रश्न
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Advertisements
उत्तर
Let `I = int (x^3 sin (tan^-1 x^4))/(1 + x^8)` dx
Put tan-1 x4 = t
or `1/(1 + x^8) * 4x^3 dx = dt`
`1/(1 + x^8). x^3 = 1/4 dt`
Hence, `I = 1/4 int sin t dt`
`= - 1/4 cos t + C`
`= - 1/4 cos (tan^-1 x^4) + C`
APPEARS IN
संबंधित प्रश्न
Evaluate :`intxlogxdx`
Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
tan2(2x – 3)
Write a value of
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).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)/(cosx - sinx).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
Fill in the Blank.
`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.
Evaluate `int (1+x+x^2/(2!))dx`
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
Evaluate:
`intsqrt(sec x/2 - 1)dx`
