Advertisements
Advertisements
प्रश्न
Integrate the function `x^2/(1 - x^6)`
Advertisements
उत्तर
Let `I = x^2/(1 - x^6) dx`
`= int x^2/(1 - (x^3)^2) dx`
Put x3 = t
3x2 dx = dt ⇒ x2 dx = `1/3` dt
`therefore I = 1/3 int dt/(1 - t^2)`
`= 1/3 . 1/2 log abs ((1 + t)/(1 - t)) + C`
`= 1/6 log abs ((1 + t)/(1 - t)) + C`
`= 1/6 log abs ((1 + x^3)/(1 - x^3)) + C` `...[∵ int dx/(a^2 - x^2) = 1/(2a) log |(a + x) /(a - x)|+C]`
APPEARS IN
संबंधित प्रश्न
Evaluate: `int(5x-2)/(1+2x+3x^2)dx`
Evaluate : ` int x^2/((x^2+4)(x^2+9))dx`
find : `int(3x+1)sqrt(4-3x-2x^2)dx`
Evaluate:
`int((x+3)e^x)/((x+5)^3)dx`
Integrate the function `(3x^2)/(x^6 + 1)`
Integrate the function `(x - 1)/sqrt(x^2 - 1)`
Integrate the function `1/sqrt(x^2 +2x + 2)`
Integrate the function `1/(9x^2 + 6x + 5)`
Integrate the function `1/sqrt(8+3x - x^2)`
Integrate the function `1/sqrt((x - a)(x - b))`
Integrate the function `(x+2)/sqrt(x^2 + 2x + 3)`
`int dx/sqrt(9x - 4x^2)` equals:
Integrate the function:
`sqrt(1- 4x^2)`
Integrate the function:
`sqrt(x^2 + 4x +1)`
Integrate the function:
`sqrt(x^2 + 4x - 5)`
Integrate the function:
`sqrt(x^2 + 3x)`
`int sqrt(x^2 - 8x + 7) dx` is equal to ______.
Find `int dx/(5 - 8x - x^2)`
\[\int\frac{1 + x + x^2}{x^2 \left( 1 + x \right)} \text{ dx}\]
Find : \[\int\left( 2x + 5 \right)\sqrt{10 - 4x - 3 x^2}dx\] .
Find:
`int_(-pi/4)^0 (1+tan"x")/(1-tan"x") "dx"`
If θ f(x) = `int_0^x t sin t dt` then `f^1(x)` is
Find: `int (dx)/(x^2 - 6x + 13)`
`int (a^x - b^x)^2/(a^xb^x)dx` equals ______.
Evaluate \[\int \frac{dx}{\sqrt{x^2+a^2}}\].
Which factorization is used before applying partial fractions to \[\frac{1}{x^2-a^2}\]?
Which trigonometric substitution is suitable for \[a^2-x^2\] and \[\sqrt{a^2-x^2}\]?
Which trigonometric substitution is suitable for \[x^2+a^2\] and \[\sqrt{x^2+a^2}\]?
Which trigonometric substitution is suitable for \[x^2-a^2\] and \[\sqrt{x^2-a^2}\]?
What is the completed-square form of \[x^2-6x+13\]?
Evaluate \[\int\frac{dx}{x^2-6x+13}\].
Which is the correct split for \[\int\frac{x+2}{2x^2+6x+5}\,dx\]?
