∫ ( 2 + s e c x ) s e c x ( 1 + 2 s e c x ) 2 d x Options: A . &nbsp12cosec x+cot x+C B . &nbsp2cosec x+cot x+C C . &nbsp12cosec x−cot x+C D . &nbsp2cosec x−cot x+C

Answer: Option A : A ∫ ( 2 c o s x + 1 ) ( 2 + c o s x ) 2 d x = ∫ ( 2 + c o s x ) c o s x + s i n 2 x ( 2 + c o s x ) 2 d x = ∫ c o s x 2 + c o s x d x − ∫ − s i n 2 x ( 2 + c o s x ) 2 d x = s i n x 2 + c o s x + c

∫(2+sec x)sec x(1+2sec x)2dx

Question

\int \frac{(2 + s e c x) s e c x}{(1 + 2 s e c x)^{2}} d x

Options:

A . 12cosec x+cot x+C

B . 2cosec x+cot x+C

C . 12cosec x−cot x+C

D . 2cosec x−cot x+C

Answer: Option A
:
A

\int \frac{(2 c o s x + 1)}{(2 + c o s x)^{2}} d x = \int \frac{(2 + c o s x) c o s x + s i n^{2} x}{(2 + c o s x)^{2}} d x = \int \frac{c o s x}{2 + c o s x} d x - \int \frac{- s i n^{2} x}{(2 + c o s x)^{2}} d x = \frac{s i n x}{2 + c o s x} + c

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. If Φ(x)=limn→∞xn−x−nxn+x−n,0<x<1,ϵN, then ∫(sin−1x)(&....If Φ(x)=limn→∞xn−x−nxn+x−n,0<x<1,ϵN, then ∫(sin−1x)(Φ(x))dx is equal to

Question 2. ∫etan−1x(1+x2)[(sec−1√1+x2)2+cos−1(1−x21+x2)]dx(x>0)....

Question 3. ∫√1+3√x3√x2dx is equal to....

Question 4. Let g(x) be an antiderivative for f(x). Then In (1+(g(x))2) is an antiderivate for....

Question 5. If ∫dxx√1−x3=a log∣∣∣√1−x3−1√1−x3+1&#x....If ∫dxx√1−x3=a log∣∣∣√1−x3−1√1−x3+1∣∣∣+C then a =

Question 6. If ∫dxx√1−x3=aln(√1−x3+b−√1−x3+1)+k, then....

Question 7. Sin3x(cos4x+3cos2x+1)tan−1(secx+cosx)dx=....

Question 8. ∫x{f(x2)g′′(x2)−f′′(x2)g(x2)}dx....

Question 9. If ∫cos 8x+1tan 2x−cot 2xdx=a cos 8x+C, then....

Question 10. The anti – derivative of the function (3x + 4) |sin x|, when 0<x<π, is given by....

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0

Submit Solution

More Questions on This Topic :

Latest Videos

Latest Test Papers