To determine
Evaluate the integral of ∫ex(4+ex)5.
Answer
(4+ex)66+c.
Explanation
Given: ∫ex(4+ex)5.
Consider y=∫ex(4+ex)5
Now substitute the value 4+ex=t so the derivative is.
dt=exdxexdx=dt
And,
∫ex(4+ex)5=∫t5dt=t5+15+1+c=t66+c
Now put the value of t get.
=(4+ex)66+c
Conclusion: Hence, the integral of ∫ex(4+ex)5 is (4+ex)66+c.