Advertisements
Advertisements
Question
Integrate the function `x^2/sqrt(x^6 + a^6)`
Advertisements
Solution
Let `I = x^2/sqrt(x^6 + a^6) dx`
`= int x^2/sqrt((x^3)^2 + (a^3)^2) dx`
Put x3 = t
3x2 dx = dt ⇒ x2 dx = `1/3` dt
`therefore I = 1/3 int dt/sqrt(t^2 + (a^3)^2)`
`= 1/3 log [t + sqrt (t^2 + a^6)] + C` `...[∵ int dx/ sqrt(x^2 + a^2) = log |x + sqrt (x^2 + a^2)| + C]`
`= 1/3 log [x^3 + sqrt(x^6 + a^6)] + C`
APPEARS IN
RELATED QUESTIONS
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`
Integrate the function `(3x^2)/(x^6 + 1)`
Integrate the function `1/sqrt(1+4x^2)`
Integrate the function `x^2/(1 - x^6)`
Integrate the function `(sec^2 x)/sqrt(tan^2 x + 4)`
Integrate the function `1/sqrt(7 - 6x - x^2)`
Integrate the function `1/sqrt((x -1)(x - 2))`
Integrate the function `1/sqrt((x - a)(x - b))`
Integrate the function `(4x+ 1)/sqrt(2x^2 + x - 3)`
Integrate the function `(5x - 2)/(1 + 2x + 3x^2)`
Integrate the function `(x + 2)/sqrt(4x - x^2)`
Integrate the function `(x+2)/sqrt(x^2 + 2x + 3)`
Integrate the function `(5x + 3)/sqrt(x^2 + 4x + 10)`
`int dx/sqrt(9x - 4x^2)` equals:
Integrate the function:
`sqrt(1-4x - x^2)`
Integrate the function:
`sqrt(1+ 3x - x^2)`
Integrate the function:
`sqrt(1+ x^2/9)`
`int sqrt(1+ x^2) dx` is equal to ______.
`int sqrt(x^2 - 8x + 7) dx` is equal to ______.
Evaluate : `int_2^3 3^x dx`
Find `int (2x)/(x^2 + 1)(x^2 + 2)^2 dx`
\[\int\frac{8x + 13}{\sqrt{4x + 7}} \text{ dx }\]
Find : \[\int\left( 2x + 5 \right)\sqrt{10 - 4x - 3 x^2}dx\] .
If θ f(x) = `int_0^x t sin t dt` then `f^1(x)` is
`int (a^x - b^x)^2/(a^xb^x)dx` equals ______.
