Advertisements
Advertisements
प्रश्न
`int x^7/(1 + x^4)^2 "d"x`
Advertisements
उत्तर
Let I = `int x^7/(1 + x^4)^2 "d"x`
= `int (x^4*x^3)/(1 + x^4)^2 "d"x`
Put 1 + x4 = t
∴ 4x3 dx = dt
∴ x3 dx = `1/4 "dt"`
∴ I = `1/4 int (("t" - 1))/"t"^2 "dt"`
= `1/4(int 1/"t" "dt" -int 1/"t"^2 "dt")`
= `1/4[log|"t"| - "t"^-1/(-1)] + "c"`
∴ `1/4[log|1 + x^4| + 1/(1 + x^4)] + "c"`
APPEARS IN
संबंधित प्रश्न
Find : `int x^2/(x^4+x^2-2) dx`
Evaluate: `∫8/((x+2)(x^2+4))dx`
Integrate the rational function:
`x/((x + 1)(x+ 2))`
Integrate the rational function:
`1/(x^2 - 9)`
Integrate the rational function:
`(1 - x^2)/(x(1-2x))`
Integrate the rational function:
`(2x - 3)/((x^2 -1)(2x + 3))`
Integrate the rational function:
`2/((1-x)(1+x^2))`
Integrate the rational function:
`(cos x)/((1-sinx)(2 - sin x))` [Hint: Put sin x = t]
Integrate the rational function:
`((x^2 +1)(x^2 + 2))/((x^2 + 3)(x^2+ 4))`
Integrate the rational function:
`(2x)/((x^2 + 1)(x^2 + 3))`
`int (xdx)/((x - 1)(x - 2))` equals:
Evaluate : `∫(x+1)/((x+2)(x+3))dx`
Integrate the following w.r.t. x : `(x^2 + 2)/((x - 1)(x + 2)(x + 3)`
Integrate the following w.r.t. x : `(12x + 3)/(6x^2 + 13x - 63)`
Integrate the following w.r.t. x : `2^x/(4^x - 3 * 2^x - 4`
Integrate the following w.r.t. x : `(5x^2 + 20x + 6)/(x^3 + 2x ^2 + x)`
Integrate the following w.r.t. x : `(1)/(sin2x + cosx)`
Integrate the following w.r.t. x : `(2log x + 3)/(x(3 log x + 2)[(logx)^2 + 1]`
Integrate the following with respect to the respective variable : `(cos 7x - cos8x)/(1 + 2 cos 5x)`
Integrate the following with respect to the respective variable : `cot^-1 ((1 + sinx)/cosx)`
State whether the following statement is True or False.
If `int (("x - 1") "dx")/(("x + 1")("x - 2"))` = A log |x + 1| + B log |x - 2| + c, then A + B = 1.
Evaluate: `int (1 + log "x")/("x"(3 + log "x")(2 + 3 log "x"))` dx
`int (2x - 7)/sqrt(4x- 1) dx`
`int x^2sqrt("a"^2 - x^6) "d"x`
`int 1/(4x^2 - 20x + 17) "d"x`
`int 1/(2 + cosx - sinx) "d"x`
`int "e"^x ((1 + x^2))/(1 + x)^2 "d"x`
`int (6x^3 + 5x^2 - 7)/(3x^2 - 2x - 1) "d"x`
`int x^3tan^(-1)x "d"x`
`int x sin2x cos5x "d"x`
`int (x + sinx)/(1 - cosx) "d"x`
`int x^2/((x^2 + 1)(x^2 - 2)(x^2 + 3)) "d"x`
`int ("d"x)/(x^3 - 1)`
Evaluate:
`int (5e^x)/((e^x + 1)(e^(2x) + 9)) dx`
Choose the correct alternative:
`int (x + 2)/(2x^2 + 6x + 5) "d"x = "p"int (4x + 6)/(2x^2 + 6x + 5) "d"x + 1/2 int 1/(2x^2 + 6x + 5)"d"x`, then p = ?
If f'(x) = `1/x + x` and f(1) = `5/2`, then f(x) = log x + `x^2/2` + ______ + c
Evaluate `int x log x "d"x`
`int 1/(4x^2 - 20x + 17) "d"x`
Evaluate the following:
`int x^2/(1 - x^4) "d"x` put x2 = t
Evaluate the following:
`int_"0"^pi (x"d"x)/(1 + sin x)`
Evaluate: `int_-2^1 sqrt(5 - 4x - x^2)dx`
If `int 1/((x^2 + 4)(x^2 + 9))dx = A tan^-1 x/2 + B tan^-1(x/3) + C`, then A – B = ______.
If `intsqrt((x - 5)/(x - 7))dx = Asqrt(x^2 - 12x + 35) + log|x| - 6 + sqrt(x^2 - 12x + 35) + C|`, then A = ______.
Evaluate`int(5x^2-6x+3)/(2x-3)dx`
Evaluate:
`int (x + 7)/(x^2 + 4x + 7)dx`
Value of ∫ `(x^2 + 1)/((x − 1)(x − 2))`dx is ______.
