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NCERT Class XII Mathematics Chapter - - Solutions

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Exercise - 7.6
Integrate the functions in Exercises 134 to 155.
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Question : 145 of 271
Marks: +1, -0
xsec⁡2xx \sec^2 x
Solution:  
Let I=∫xsec⁡2xdxI=\int x\sec^2 x dx
=x∫sec⁡2xdx−∫(ddxx⋅∫sec⁡2xdx)dx=x\int\sec^2 x dx-\int\left(\frac{d}{dx}x\cdot\int\sec^2 x dx\right)dx
=xtan⁡x−∫1⋅tan⁡xdx=x\tan x-\int 1\cdot\tan x dx
=xtan⁡x+log⁡cos⁡x+C=x\tan x+\log\cos x+C
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