A) \[\frac{{{\sec }^{n}}x}{n}+c\]
B) \[\frac{{{\sec }^{n-1}}x}{n-1}+c\]
C) \[\frac{{{\tan }^{n}}x}{n}+c\]
D) \[\frac{{{\tan }^{n-1}}x}{n-1}+c\] Where ?c? is a constant of integration.
Correct Answer: A
Solution :
[a] Let \[I=\int{{{\sec }^{n}}x\tan xdx.}\] Put, \[\sec x=t\Rightarrow \sec x\tan xdx=dt\] \[\therefore I=\int{{{t}^{n}}.\frac{dt}{t}}\] \[=\int{{{t}^{n-1}}dt=\frac{{{t}^{n}}}{n}+c=\frac{{{\sec }^{n}}x}{n}+c}\] Where ?c? is a constant of integration.
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