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NCERT Class XII Mathematics Chapter - - Solutions

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Exercise - 7.2
Integrate the functions in Exercises 23 to 59.
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Question : 44 of 271
Marks: +1, -0
sec⁡2(7−4x)\sec^2(7-4x)
Solution:  
Let I=∫sec⁡2(7−4x)dxI=\int\sec^2(7-4x)dx
Put 7−4x=t⇒−4dx=dt7 -4x = t \Rightarrow -4dx = dt
∴I=−14∫sec⁡2tdt\therefore I = -\frac{1}{4}\int\sec^2 t dt =14tan⁡t+C=\frac{1}{4}\tan t + C =−14tan⁡(7−4x)+C=-\frac{1}{4}\tan(7-4x)+C
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