Find the logarithmic derivative and then determine the percentage rate of change of the function at the points indicated \( f(t)=e^{0.2 t^{2}} \) at \( t=3 \) and \( t=7 \) The logarithmic derivative is \( \square \). The percentage rate of change of \( f(t) \) at \( t=3 \) is \( \square \% \). (Type an integer or a decimal.) The percentage rate of change of \( f(t) \) at \( t=7 \) is \( \square \% \). (Type an integer or a decimal.)

Find the general indefinite integral. (Use \( C \) for the constant of integration. \[ \int 5 v\left(v^{2}+2\right)^{2} d v \]

\( \int \frac { d x } { 4 x ^ { 2 } + 25 } \)

\( \int _{}^{}\frac{x^{2}}{\sqrt [4]{x^{3}}+2} d x \)

Resuelva las Integrales: a) \( \left.\int\left(3 x^{1 / 2}+7\right) d x, b\right) \int \frac{2 x+1}{\sqrt{x^{2}}+1} d x, \int_{0}^{2}\left(3 x^{2}+2 x\right) d x \) Valor (30 puntos)

Derivar las siguientes funciones 6. \( f(x)=\left(x^{2}-1\right)\left(3 x^{2}-6 x+5\right)-(x+4)\left(4 x^{2}-2 x+1\right) \) 7. \( f(x)=\frac{3}{2}(\sqrt{x}-4)(4 x-5) \) 8. \( f(x)=(2 x-1)(3 x+4)(x+7) \) 9. \( f(x)=\frac{8 x^{2}-2 x+1}{x^{2}-5 x} \) 10. \( f(x)=\frac{x^{2}-4 x+3}{2 x^{2}-3 x+2} \)