Home
Class 12
MATHS
int (dx)/((cos ^(2)x-3sin^(2)x))=?...

`int (dx)/((cos ^(2)x-3sin^(2)x))=?`

A

`(1)/(sqrt(3))log |(sqrt(3)+tanx)/(sqrt(3)-tanx)+C`

B

`(1)/(4)log |(1-sqrt(3)+tanx)/(1+sqrt(3)-tanx)+C`

C

`(1)/(2sqrt(3))log |(1+sqrt(3)tanx)/(1-sqrt(3)tanx)|+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
On dividing Nr and Dr by `cos^(2)x,` we get
`I=int(sec^(2)x)/((1-3tan^(2)x))dx=int(dt)/((1-3t^(2))),"where " tan x=t`
`=(1)/(3) int(dt)/(((1)/(3)-t^(2)))=(1)/(3).int(dt)/({((1)/(sqrt(3)))^(2)-t^(2)})=(1)/(3).(1)/(2xx(1)/(sqrt(3)))log|((1)/(sqrt(3))+t)/((1)/(3)-t)|+C`
`=(1)/(2sqrt(3))log|(1+sqrt(3)tanx)/(1-sqrt(3)tanx)|+C.`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION USING PARTIAL FRACTIONS

    RS AGGARWAL|Exercise Objective Questions Ii|37 Videos

  • INTEGRATION USING PARTIAL FRACTIONS

    RS AGGARWAL|Exercise Exercise 15B|40 Videos

  • INDEFINITE INTEGRAL

    RS AGGARWAL|Exercise Objective Questions|41 Videos

  • INVERSE TRIGNOMETRIC FUNCTIONS

    RS AGGARWAL|Exercise Objective Questons|57 Videos

Similar Questions

Explore conceptually related problems

int(1)/(cos^(2) x-3 sin^(2) x)dx

int((7)/(cos^(2)x)-(3)/(sin^(2)x))dx

int(dx)/(cos x*sin^(2)x)

int(sin2x)/(2cos^(2)x+3sin^(2)x)dx equals

Find the mistake of the following evaluation of the integral I=int_(0)^( pi)(dx)/(1+2sin^(2)x)I=int_(0)^( pi)(dx)/(cos^(2)x+3sin^(2)x)=int_(0)^( pi)(sec^(2)xdx)/(1+3tan^(2)x)=(1)/(sqrt(3))[tan^(-1)(sqrt(3)tan x)]_(0)^( pi)=0

int(sin x)/(cos^(2)x)dx

int(sin x)/(cos^(2)x)dx

If int(dx)/(cos2x+3sin^(2)x)=(1)/(a)tan^(-1)(b tanx)+c, then ab=

(i) int(cos^(3) x+ sin^(3) x)/(sin^(2) x.cos ^(2) x)dx " "(ii) int(cos2x)/(cos^(2) x sin^(2)x) dx

Evaluate: (i) int(sin2x)/(a cos^(2)x+b sin^(2)x)dx (ii) int(cos x)/(2+3sin x)dx