Question
Evaluate the following integrals:
$\int\frac{1}{1-\sin\text{x}}\text{dx}$
$\int\frac{1}{1-\sin\text{x}}\text{dx}$
$=\int\frac{(1+\sin\text{x})}{(1-\sin\text{x})\times(1+\sin\text{x})}\text{dx}$
$=\Big(\frac{1+\sin\text{x}}{1-\sin^2\text{x}}\Big)\text{dx}$
$=\int\Big(\frac{1+\sin\text{x}}{\cos^2\text{x}}\Big)\text{dx}$
$=\int\Big(\frac{1}{\cos^2\text{x}}+\frac{\sin\text{x}}{\cos\text{x}}\times\frac{1}{\cos\text{x}}\Big)\text{dx}$
$=\int(\sec^2\text{x}+\sec\text{x}\tan\text{x})\text{dx}$
$=\tan\text{x}+\sec\text{x}+\text{C}$
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$\vec{\text{r}}=2\hat{\text{i}}-\hat{\text{j}}-56\hat{\text{k}}+\mu\Big(3\hat{\text{i}}-5\hat{\text{j}}-4\hat{\text{k}}\Big)$