Question

Integrate the following function:

Answer 1

Answer: None of these

Explanation:

First term

`\int 12e^(12t) \text{ } dt=12 \int e^(12t) \text{ } dt=e^(12t)+C`

Second term

`\int \sqrt[3]{27t} \text{ } dt=3\int t^(1/3) \text{ } dt=(9)/(4)\sqrt[3]{t^4}+C`

Third term

`\int (5)/(t) \text{ } dt=5 \int (1)/(t) \text{ } dt=5\ln t+C`

Fourth term

`\int 15 \text{ } dt=15t+C`

Adding these integrals, we get

`\int g(t) \text{ } dt=e^(12t)+(9)/(4)\sqrt[3]{t^4}+5\ln t+15t+C`

which matches none of the options.