Question

Evaluate the integral. ∫ 1−e x

1+5e x
dx Select the correct answer. a. 6x−5ln(e x
−1)+C b. x+8ln(e x
−1)+C c. 8x+6ln∣e x
−1∣+C d. x−6ln∣e x
−1∣+C e. 6x−5ln(e x
+1)+C

Answer 1

Explanation:

Let y=∑ n=0

[infinity]

​

c n

​

x n

. Substitute this expression into the following differential equation and simplify to find the recurrence relations. Select two answers that represent the complete recurrence relation. 2y ′

+xy=0 c 1

​

=0 c 1

​

=−c 0

​

c k+1

​

= 2(k−1)

c k−1

​

​

,k=0,1,2,⋯ c k+1

​

=− k+1

c k

​

​

,k=1,2,3,⋯ c 1

​

= 2

1

​

c 0

​

c k+1

​

=− 2(k+1)

c k−1

​

​

,k=1,2,3,⋯ c 0

​

=0