Home
Class 12
MATHS
Evaluate int (dx)/(xsqrt(x^6-1))...

Evaluate `int (dx)/(xsqrt(x^6-1))`

Text Solution

Verified by Experts

Let `x^3 = t`
Then, `3x^2dx = dt`
`:. int dx/(xsqrt(x^6-1)) = int (x^2dx)/(x^3sqrt(x^6-1)`
`=1/3 int dt/(tsqrt(t^2-1))`
Now, let `t = sec theta`
Then, `dt = sectheta tantheta d theta`
So, our integral becomes,
`1/3 int (sectheta tan theta )/(sectheta tan theta)d theta`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

Evaluate : int(dx)/(xsqrt(x^4-1))

int (dx)/(xsqrt(x^(4)-1))

int(dx)/(xsqrt(x^(6)-16))=

int(dx)/(xsqrt(x^(6)-16))=

int (dx)/(xsqrt(x+1))

int(dx)/(xsqrt(x^(n)+1))

int (dx)/(xsqrt(x^(2)+x+1))

int (dx)/(xsqrt(1+x^(3)))

Evaluate: int(x^2+1)/(xsqrt(x^2+1))dx