+91-705-589-3577
FlagBACK
Flag Integral Calculus> integrate the following ∫dx/(5 +7 cos x+s...
question mark

integrate the following
∫dx/(5 +7 cos x+sin x)
the answer is
1/5 log|tan x/2+2|/|tan x/2-2| + c
but how please solve?

apurva , 6 Years ago
Grade 11
anser 1 Answers
Aditya Gupta
hello apurva. this is an ez ques.
we need to use the following standard formulae: sinx= 2t/(1+t^2) and cosx= (1 – t^2)/(1+t^2) where t= tan(x/2).
so we substitite t= tan(x/2) so that dt/dx= ½ *sec^2(x/2) or 2dt/dx= 1+ tan^2(x/2)= 1+t^2
so, integral J becomes
J= ∫dx/(5 +7 cos x+sin x)= ∫2dt/[5(1+t^2)+7(1 – t^2)+2t]
= 2∫dt/( –2t^2 + 2t + 12)
= ∫dt/( –t^2 + t + 6)
= – ∫dt/(t – 3)(t+2)
now you can easily use partial fractions to write 1/(t – 3)(t+2)= [1/(t – 3) – 1/(t+2)]/5 and solve it.
kindly approve :)
Last Activity: 6 Years ago
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Other Related Questions on integral calculus

question mark
The area of a square field is 640000cm2.what is its area in hectares
integral calculus
1 Answer Available

Last Activity: 3 Years ago

question mark
Please solve this integration. I am facing difficulty in it
 How to solve this. Please solve anyone. Humble request
integral calculus
1 Answer Available

Last Activity: 3 Years ago

question mark
Using laplace transform, solve d2y/dt2 + dy/dt = t2 +2t given that y=4 and y’=-2 and t=0
integral calculus
1 Answer Available

Last Activity: 3 Years ago

question mark
If 4th term of an A.p is zero, show that the 8th term is double the 6th term
 
integral calculus
1 Answer Available

Last Activity: 4 Years ago