Question

intigration of tan^2 x dx​

Answer 1

Answer:

This is very easy, and this involves the use of trig identities:

∫tan2(x)dx

Since tan2(x)=−1+sec2(x) , so we rewrite the equation as:

∫tan2(x)=∫−1+sec2(x)dx

Applying the sum rule, where ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx , so we rewrite the equation again as:

−∫1dx+∫sec2(x)dx

Solving for ∫1dx

Since ∫adx=ax , so

∫1dx=1⋅x=x

So −∫1dx=−x

Solving for ∫sec2(x)dx, which is a common integral: =tan(x) .

So −∫1dx+∫sec2(x)dx=−x+tan(x)

Adding the constant, the final answer is −x+tan(x)+C

Step-by-step explanation:

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