Question

integration of
(Cos X - sin X )
___________. (2 +2sin 2 X)
cos X + sin x
​

Answer 1

Step-by-step explanation:

ANSWER

∫

0

π/2

3+sin2x

sinx+cosx

dx.

∫

0

π/2

4−(sinx−cosx)

2

sinx+cosx

dx=∫

0

π/2

(2)

2

−(sinx−cosx)

2

d(sinx−cosx)

=

4

1

log

∣

∣

∣

∣

∣

2−(sinx−cosx)

2+(sinx−cosx)

∣

∣

∣

∣

∣

0

π

=

4

1

(log

∣

∣

∣

∣

∣

2−0

2+0

∣

∣

∣

∣

∣

−log

∣

∣

∣

∣

∣

2+1

2−1

∣

∣

∣

∣

∣

)

=

4

1

(−log

3

1

)

=

4

1

log(3)