Question
Integrate t√t+√t/t^2
Answers
GPT 3.5
To integrate the given expression, we first note that t√t can be simplified to t^(3/2) and √t can be simplified to t^(1/2).
Therefore, the expression becomes t^(3/2) + t^(1/2) / t^2.
Next, we can separate this into two integrals:
∫ t^(3/2) dt + ∫ t^(-5/2) dt
Integrating the first term gives us: (2/5)t^(5/2) + C
Integrating the second term gives us: (-2/3)t^(-3/2) + C
Therefore, the final result of integration is:
(2/5)t^(5/2) - (2/3)t^(-3/2) + C
where C is the constant of integration.
Therefore, the expression becomes t^(3/2) + t^(1/2) / t^2.
Next, we can separate this into two integrals:
∫ t^(3/2) dt + ∫ t^(-5/2) dt
Integrating the first term gives us: (2/5)t^(5/2) + C
Integrating the second term gives us: (-2/3)t^(-3/2) + C
Therefore, the final result of integration is:
(2/5)t^(5/2) - (2/3)t^(-3/2) + C
where C is the constant of integration.