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.