S(t√+√t/t^)dt

Answer 1

To integrate the given function S(t√t+√t/t^)dt, we first need to simplify the expression under the square root.

1. Recall that √a√b = √ab. Therefore, we can simplify the expression t√t to √t^3.

2. Next, the expression under the square root becomes √t^3 + √t/t^.

3. We can further simplify the expression to t^(3/2) + √(t)/t.

Now, the integral becomes:

∫ (t^(3/2) + √(t)/t) dt

= ∫ t^(3/2) dt + ∫ √(t)/t dt

= (2/5)t^(5/2) + ln|t| + C

Therefore, the integral of S(t√t+√t/t^)dt is equal to (2/5)t^(5/2) + ln|t| + C, where C is the constant of integration.