Question

integrate cos^8 x cotx.​

Answer 1

Answer:

kya kroge integrate karke jindagi toh jhand honi hi hai chahe kaise bhi ho

Answer 2

Answer:

Let I=∫cos

8

xcotx.dx

=∫cos

8

x.

sinx

cosx

.dx

Put sinx=t

∴cosxdx=dt

cos

8

x=(cos

2

x)

4

=(1−sin

2

x)

4

=(1−t

2

)

4

=1−4t

2

+6t

4

+6t

4

−4t

6

+t

8

I=∫

t

1−4t

2

+6t

4

−4t

6

+t

8

dt

=∫[

t

1

−4t+6t

3

−4t

5

+t

7

]dt

=∫

t

1

dx−4∫tdt+6∫t

3

dt−4∫t

5

dt+∫t

7

dt

=log∣t∣−4(

2

t

2

)+6(

4

t

4

)−4(

6

t

6

)+

8

t

8

+c

=log∣sinx∣−2sin

2

x+

2

3

sin

4

x−

3

2

sin

6

+

8

sin

8

x

+c