Integration (solve)
S=(t√t+√t/t^2)dt
To solve this integration problem, we can start by simplifying the expression inside the integral:
S = ∫(t√t + √t/t^2) dt
S = ∫(t^(3/2) + t^(-1/2)) dt
S = ∫t^(3/2) dt + ∫t^(-1/2) dt
Now we can use the power rule for integration:
∫x^n dx = (x^(n+1))/(n+1) + C
Applying this rule to each term in the integral:
∫t^(3/2) dt = (t^(5/2))/(5/2) + C = (2/5)t^(5/2) + C
∫t^(-1/2) dt = (t^(1/2))/(1/2) + C = 2√t + C
Therefore, the solution to the integration is:
S = (2/5)t^(5/2) + 2√t + C