Evaluate the indefinite integral

Question

∫ 5⁴ sin(5^t) dt

 

ANSWER: - 1/ln(5) * cos(5^t) + C

#29, p414

Answer 1

Based on your answer, I'm assuming when you put 5⁴ you meant 5^t.

 

Let's set u = 5^t

 

du = 5^t*ln(5) dt

 

du/ln(5) = 5^t dt

 

So now you have an integral that looks like this:

 

1/ln(5)*∫ sin(u) du

 

= 1/ln(5) * (-cos(u)) + C

 

but u = 5^t

 

So now you have:

 

-1/ln(5)*cos(5^t) + C