Question

Calculate the definite integral y = 𝑡 ^3 + 2𝑒 ^ 4𝑡 + 1/ 𝑡 + 3 sin 2𝑡)

Answer 1

$$y=\int (𝑡 ^3 + 2𝑒 ^ {4t} + \dfrac{1}{t} + 3 \sin (2𝑡))dt$$

$$=\dfrac{t^4}{4}+\dfrac{1}{2}e^{4t}+\ln|t|-\dfrac{3}{2}\cos(2t)+C$$