Advertisements
Advertisements
Question
Evaluate the following:
`int ("d"x)/(xsqrt(x^4 - 1))` (Hint: Put x2 = sec θ)
Solution
Let I = `int ("d"x)/(xsqrt(x^4 - 1))`
= `int (x"d"x)/(x^2sqrt(x^4 - 1))`
Put x2 = sec θ
∴ 2x dx = sec θ tan θ dθ
x dx = `1/2 sec theta tan theta "d"theta`
∴ I = `1/2 int (sec theta tan theta)/(sec theta sqrt(sec^2theta - 1)) "d"theta`
= `1/2 int (sectheta tan theta)/(sectheta * tan theta) "d"theta`
= `1/2 int 1 "d"theta`
= `1/2 theta + "C"`
So I = `1/2 sec^-1x^2 + "C"`
Hence, I = `1/2 sec^-1 x^2 + "C"`.
APPEARS IN
RELATED QUESTIONS
Evaluate : `int_0^3dx/(9+x^2)`
Integrate the following w.r.t. x `(x^3-3x+1)/sqrt(1-x^2)`
Evaluate the following integrals:
Evaluate the following integral :-
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Write a value of
Evaluate:\[\int\frac{\log x}{x} \text{ dx }\]
Evaluate: \[\int\frac{1}{\sqrt{1 - x^2}} \text{ dx }\]
Evaluate: \[\int\frac{1}{x^2 + 16}\text{ dx }\]
Evaluate the following:
`int ("d"x)/sqrt(16 - 9x^2)`
Evaluate the following:
`int_1^2 ("d"x)/sqrt((x - 1)(2 - x))`
