Advertisements
Advertisements
प्रश्न
Choose the correct alternative:
`int ((x^3 + 3x^2 + 3x + 1))/(x + 1)^5 "d"x` =
विकल्प
`(-1)/(x + 1) + "c"`
`((-1)/(x + 1))^5 + "c"`
log(x + 1) + c
5log(x + 5) + c
Advertisements
उत्तर
`(-1)/(x + 1) + "c"`
APPEARS IN
संबंधित प्रश्न
Find: `I=intdx/(sinx+sin2x)`
Integrate the rational function:
`2/((1-x)(1+x^2))`
`int (xdx)/((x - 1)(x - 2))` equals:
Find `int(e^x dx)/((e^x - 1)^2 (e^x + 2))`
Integrate the following w.r.t. x : `(x^2 + x - 1)/(x^2 + x - 6)`
Choose the correct options from the given alternatives :
If `int tan^3x*sec^3x*dx = (1/m)sec^mx - (1/n)sec^n x + c, "then" (m, n)` =
Integrate the following with respect to the respective variable : `(cos 7x - cos8x)/(1 + 2 cos 5x)`
Integrate the following w.r.t.x : `x^2/sqrt(1 - x^6)`
Integrate the following w.r.t.x : `(1)/((1 - cos4x)(3 - cot2x)`
Integrate the following w.r.t.x:
`x^2/((x - 1)(3x - 1)(3x - 2)`
`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^2/((x^2 + 1)(x^2 - 2)(x^2 + 3)) "d"x`
`int xcos^3x "d"x`
`int ((2logx + 3))/(x(3logx + 2)[(logx)^2 + 1]) "d"x`
Evaluate `int (2"e"^x + 5)/(2"e"^x + 1) "d"x`
Evaluate `int x log x "d"x`
Evaluate the following:
`int x^2/(1 - x^4) "d"x` put x2 = t
Evaluate the following:
`int (x^2"d"x)/(x^4 - x^2 - 12)`
If f(x) = `int(3x - 1)x(x + 1)(18x^11 + 15x^10 - 10x^9)^(1/6)dx`, where f(0) = 0, is in the form of `((18x^α + 15x^β - 10x^γ)^δ)/θ`, then (3α + 4β + 5γ + 6δ + 7θ) is ______. (Where δ is a rational number in its simplest form)
Let g : (0, ∞) `rightarrow` R be a differentiable function such that `int((x(cosx - sinx))/(e^x + 1) + (g(x)(e^x + 1 - xe^x))/(e^x + 1)^2)dx = (xg(x))/(e^x + 1) + c`, for all x > 0, where c is an arbitrary constant. Then ______.
Find: `int x^4/((x - 1)(x^2 + 1))dx`.
Integration by partial fractions is a method used to integrate which functions?
A proper rational function can be expressed as a sum of simpler rational functions called what?
Which decomposition is correct for \[\frac{x^{2}+1}{x^{2}-5x+6}\]?
What must be included for a repeated linear factor?
