Question

Evaluate :∫sec^2(7-4x)dx

Answer 1

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Given I =∫sec2⁡(7−4x).

Put 7-4x=t.

dt=-4d⇒dx=−dt4.

Now substituting for x and dx we get,

I=∫sec2⁡t(−dt4).

=−14∫sec2⁡tdt.

On integrating we get,

−14tan⁡t+c.

Substituting back for t we get,
 
∫sec2⁡(7−4x)=14tan⁡(7−4x)+c.
 
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Hope it will help u..........