Integrals

Determine the integral of the given function: $\int t^{3}\left(t^{4}-6\right)^{4} d t=$

Evaluate the following integral. \[ \int_{\ln (3 \pi / 2)}^{\ln (11 \pi / 6)} 10 e^{v} \cos e^{v} d v \]

Evaluate the following indefinite integral. \[ \int \frac{10}{\sqrt{x}} d x \]

Evaluate the integral: \(\int (3x^2-2x+1)e^{x^3-x^2+x} dx\)

Suppose $f(x)=\left\{\begin{array}{l}x^{2}-4 x \text { for } x<-4 \\ 4 x-x^{2} \text { for } x \geq-4\end{array}\right.$ then \[ \int_{-16}^{4} f(x) d x \] is equal to... $\int_{-16}^{-4}\left(x^{2}-4 x\right) d x+\int_{-4}^{4}\left(4 x-x^{2}\right) d x$ B. $\int_{-16}^{0}\left(x^{2}-4 x\right) d x+\int_{0}^{4}\left(4 x-x^{2}\right) d x$ C. $\int_{-16}^{-4}\left(4 x-x^{2}\right) d x+\int_{-4}^{4}\left(x^{2}-4 x\right) d x$ D. $\int_{-16}^{-4}\left(x^{2}-4 x\right) d x+\int_{-4}^{4}\left(x^{2}-4 x\right) d x$ E. $\int_{-16}^{0}\left(4 x-x^{2}\right) d x+\int_{0}^{4}\left(x^{2}-4 x\right) d x$