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Question

Question: \[\int_{}^{}{x\sec^{2}xdx =}\]...

∫xsec⁡2xdx=\int_{}^{}{x\sec^{2}xdx =}

A

tan⁡x+logcosx+c\tan x + {logcos}x + c

B

x22sec⁡2x+logcosx+c\frac{x^{2}}{2}\sec^{2}x + {logcos}x + c

C

xtan⁡x+logsecx+cx\tan x + {logsec}x + c

D

xtan⁡x+logcosx+cx\tan x + {logcos}x + c

Answer

xtan⁡x+logsecx+cx\tan x + {logsec}x + c

Explanation

Solution

∫xsec⁡2xdx=xtan⁡x−∫tan⁡xdx\int_{}^{}{x\sec^{2}xdx = x\tan x - \int_{}^{}{\tan xdx}} =xtan⁡x+log⁡(cos⁡x)+c= x\tan x + \log(\cos x) + c