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 PUBLICATION|Exercise Subjective Type|6 Videos
INDEFINITE INTEGRATION
CENGAGE PUBLICATION|Exercise Comprehension Type|2 Videos
INDEFINITE INTEGRATION
CENGAGE PUBLICATION|Exercise Archives JEE ADVANCED (Single Correct Answer Type)|1 Videos
HYPERBOLA
CENGAGE PUBLICATION|Exercise COMPREHENSION TYPE|2 Videos
INEQUALITIES AND MODULUS
CENGAGE PUBLICATION|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

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

Prove that, int(cos 5x + cos4x)/(1-2cos 3x)dx= -(1/2 sin2x + sinx)+c

Evaluate int dx/(sin x cos x)

Evaluate : int cos^(3)2x dx

Evaluate: int(cos2x + 2 sin^2 x)/(cos^2 x)dx

Prove : int (cos x - cos 2x)/(1-cosx) dx = x + 2 sin x + c

Evaluate: int1/(sin^4x+cos^4x)dx

Evaluate: int(sin x dx)/(cos 2x)

Evaluate : int cos^(2) 2x dx

Evaluate: int(sinx)/(cos2x)\ dx

CENGAGE PUBLICATION-INDEFINITE INTEGRATION-Single Correct Answer Type

Evaluate: int(cos5x+cos4x)/(1-2cos3x)\ dx
07:19
|
int(secx."cosec"x)/(2cotx-secx"cosec x")dx is equal to
02:55
|
Evaluate: int(1)/(x)ln((x)/(e^(x)))dx=
02:46
|
Evaluate int((cosx)^(n-1))/((sinx)^(n+1))dx= (A) -cot^n x/n+...
02:58
|
If int x^(26).(x-1)^(17).(5x-3)dx=(x^(27).(x-1)^(18))/(k)+C where C is...
06:18
|
If int(x+(cos^(-1)3x)^(2))/(sqrt(1-9x^(2)))dx=Asqrt(1-9x^(2))+B(cos^(-...
06:20
|
If int(tan^(9)x)dx=f(x)+log|cosx|, where f(x) is a polynomial of degre...
03:19
|
int(cosx-sinx+1-x)/(e^(x)+sinx+x)dx=log(e)(f(x))+g(x)+C where C is the...
02:59
|
Evaluate:int(x+x^(2/3)+x^(1/6))/(x(1+x^(1/3)))dx equals
04:55
|
int(e^(x)(x-2))/(x(x^(2)+e^(x)))dx AAx gt0 is equal to
03:51
|
If x^2!=n pi-1, n in N. Then, the value of int x sqrt((2sin(x^2+1)-sin...
04:35
|
The value of int("cosec x")/(cos^(2)(1+logtan.(x)/(2)))dx is
02:43
|
Evaluate: int(dx)/(xsqrt(x^(6)-16))=
02:29
|
int (dx)/(cos (2 x)cos (4x)) is equal to
05:52
|
intx2^(ln(x^(2)+1))dx is equal to
02:25
|
If int(sinx)/(sin(x-(pi)/(4)))dx=Af(x)+(1)/(sqrt2)log[|sinx-cosx|]+c, ...
04:09
|
Evaluate: int(sqrt((cosx)/(x))-sqrt((x)/(cosx))sinx)dx equals
02:32
|
Evaluate: int((2x+1))/((x^(2)+4x+1)^(3//2))dx
05:20
|
If int((2x+3)dx)/(x(x+1)(x+2)(x+3)+1)=C-(1)/(f(x)) where f(x) is of th...
02:54
|
The integral intsqrt(cotx)e^(sqrt(sinx))sqrt(cosx)dx equals
03:33
|