Evaluate: int(cos5x+cos4x)/(1-2cos3x)\ d...

Evaluate: `int(cos5x+cos4x)/(1-2cos3x)\ dx`

A

`-((sin2x)/(2)+cosx)+C`

B

`-((sin2x)/(2)+cosx)+C`

C

`-((cos2x)/(2)+cosx)+C`

D

`-((sin2x)/(2)+sinx)+C`

Text Solution

Verified by Experts

The correct Answer is:

D

`int(cos5x+cos4x)/(1-2cos3x)dx`
`=int(2cos.(9x)/(2)cos.(x)/(2)dx)/(1-2(2cos^(2)((3x)/(2))-1))`
`=int(2cos.(x)/(2)(4cos^(3),(3x)/(2)-3cos.(3x)/(2)))/(3-4cos^(2).(3x)/(2))dx`
`=-int2cos.(3x)/(2)cos.(x)/(2)dx=-intcos2xdx-int cosxdx`
`=-((sin2x)/(2)+sinx)+C`

Doubtnut Promotions Banner Desktop Dark

Doubtnut Promotions Banner Mobile Dark

|

Topper's Solved these Questions

INDEFINITE INTEGRATION
CENGAGE|Exercise Subjective Type|6 Videos
INDEFINITE INTEGRATION
CENGAGE|Exercise Comprehension Type|2 Videos
INDEFINITE INTEGRATION
CENGAGE|Exercise JEE Advanced Previous Year|1 Videos
HYPERBOLA
CENGAGE|Exercise JEE Advanced Previous Year|14 Videos
INEQUALITIES AND MODULUS
CENGAGE|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

Evaluate: int(cos x-cos2x)/(1-cos x)dx

Evaluate int(cosx-cos2 x)/(1-cos x) dx

Knowledge Check

The value of int(cos 5x+cos 4x)/(1-2 cos 3 x)dx , is

A

`sin x+ sin2x+C`

B

`sin x-(sin 2x)/(2)+C`

C

`-sin x-(sin2x)/(2)+C`

D

None of these

Similar Questions

Explore conceptually related problems

Evaluate: int(cos x)/(cos3x)dx

int(cos x-cos2x)/(1-cos x)*dx

Evaluate: int(cos4x-cos2x)/(sin4x-sin2x)dx

Evaluate: int(cos x)/((1)/(4)-cos^(2)x)dx

int(cos3x-cos2x)/(cos x)dx

Evaluate: int(1)/(cos3x-cos x)dx

Evaluate: int(1)/(cos3x-cos x)dx

CENGAGE-INDEFINITE INTEGRATION-Single Correct Answer Type

Evaluate: int(cos5x+cos4x)/(1-2cos3x)\ dx
04:44
|
int(secx."cosec"x)/(2cotx-secx"cosec x")dx di equal to
02:10
|
int(1)/(x)ln((x)/(e^(x)))dx=
01:57
|
int((cosx)^(n-1))/((sinx)^(n+1))dx= (A) -cot^n x/n+c (B) -...
02:24
|
If int x^(26).(x-1)^(17).(5x-3)dx=(x^(27).(x-1)^(18))/(k)+C where C is...
02:57
|
If int(x+(cos^(-1)3x)^(2))/(sqrt(1-9x^(2)))dx=Asqrt(1-9x^(2))+B(cos^(-...
05:02
|
If int(tan^(9)x)dx=f(x)+log|cosx|, where f(x) is a polynomial of degre...
04:01
|
int(cosx-sinx+1-x)/(e^(x)+sinx+x)dx=log(e)(f(x))+g(x)+C where C is the...
03:42
|
int(x+x^(2/3)+x^(1/6))/(x(1+x^(1/3)))dx equals
03:26
|
int(e^(x)(x-2))/(x(x^(2)+e^(x)))dx AAx gt0 is equal to
03:55
|
If x^2!=n pi-1, n in N. Then, the value of int x sqrt((2sin(x^2+1)-sin...
03:29
|
The value of int("cosec x")/(cos^(2)(1+logtan.(x)/(2)))dx is
03:22
|
int(dx)/(xsqrt(x^(6)-16))=
01:47
|
int(dx)/(cos(2x)cos(4x))=
06:38
|
int x.2^(ln(x^(2)+1))dx is equal to
02:21
|
If int(sinx)/(sin(x-(pi)/(4)))dx=Af(x)+(1)/(sqrt2)log[|sinx-cosx|]+c, ...
04:13
|
int(sqrt((cosx)/(x))-sqrt((x)/(cosx))sinx)dx equals
02:15
|
int((2x+1))/((x^(2)+4x+1)^(3//2))dx
04:05
|
If int((2x+3)dx)/(x(x+1)(x+2)(x+3)+1)=C-(1)/(f(x)) where f(x) is of th...
02:40
|
The integral intsqrt(cotx)e^(sqrt(sinx))sqrt(cosx)dx equals
02:13
|