Home
Class 12
MATHS
Evaluate : int " cos"^(-1) (1/x) dx...

Evaluate : `int " cos"^(-1) (1/x) dx`

Text Solution

Verified by Experts

`int " cos"^(-1)(1)/(x) dx`
`=int" sec"^(-1) x. dx =int " sec"^(-1)x. 1dx`
`=sec^(-1) x. int1dx =int{(d)/(dx) sec^(-1) x. int1dx } dx`
`"(Tanking" sec^(-1) " x as 1st functions "`
` = x sec^(-1) x - int (1)/(xsqrt(x^(2)-1)). x dx`
`= x sec^(-1) x - int (1)/(sqrt(x^(2)-1)^(2)) dx `
`= x sec^(-1) x - log |x + sqrt( x^(2) -1) |+C`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    NAGEEN PRAKASHAN|Exercise Exercise 7a|14 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN|Exercise Exercise 7b|26 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|18 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise (prove That )|9 Videos

Similar Questions

Explore conceptually related problems

Evaluate: int cos^(-1)(sin x)dx

Evaluate : int(x cos^(-1)x)/(1-x^(2))dx

Evaluate: int(cos^-1x)/x^2dx

evaluate int cos^(-1)sqrt((x)/(a+x))dx

Evaluate int(cos^(-1)x)/(x^(2))dx

Evaluate: int(1)/(sin x cos^(3)x)dx

Evaluate : int(1)/(x^(2)"cos"^(2)((1)/(x)))dx

Evaluate : int (1)/(" sin"^(2) x " cos"^(2) x ") ") " dx "

Evaluate: int1/(sinx(2cos^(2)x-1))dx