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Multivariable Calculus

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Find the Indefinite Integral

MVCALC-I1YLWA

What is the indefinite integral of the vector-valued function:

$${\bf r}(t)=\frac{1}{1-t}{\bf i} + e^t {\bf j}+{\bf k}$$

...with respect to $t$?

A

This function does not have an elementary integral.

B

$\ln \left(\frac{1}{1-t}\right) {\bf i} +e^t{\bf j} $

C

$\ln \left(\frac{1}{1-t}\right) {\bf i} +e^t{\bf j} +t{\bf k}$

D

$\ln (1-t) {\bf i} +e^t{\bf j} +t{\bf k}$

E

$\frac{1}{(1-t)^2} {\bf i}$