A) \[\frac{1}{3}{{\sec }^{3}}x-\sec x+c\]
B) \[{{\sec }^{3}}x-\sec x+c\]
C) \[\frac{1}{3}{{\sec }^{3}}x+\sec x+c\]
D) None of these
Correct Answer: A
Solution :
\[\int_{{}}^{{}}{\sec x{{\tan }^{3}}x\ dx=\int_{{}}^{{}}{\sec x({{\sec }^{2}}x-1)\tan x\ dx}}\] \[=\int_{{}}^{{}}{\sec x\tan x{{\sec }^{2}}x\ dx}-\int_{{}}^{{}}{\sec x\tan x\ dx}\] \[=\frac{{{\sec }^{3}}x}{3}-\sec x+c\], (Putting \[\sec x=t\] in first part).
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