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(Tanx)^2(Secx)
The purpose of integration is to find the antiderivative of a given function. In this case, we are trying to find the function that, when differentiated, will give us (Tanx)^2(Secx).
The formula for integrating (Tanx)^2(Secx) is ∫(Tanx)^2(Secx) dx = ∫(Secx)^2 dx - C. This can also be written as ∫(1 + Tan^2x)(Secx) dx.
Yes, (Tanx)^2(Secx) can be simplified to (Secx)^2 - 1 before integrating. This will make the integration process easier.
Yes, the method for integrating (Tanx)^2(Secx) is called u-substitution. This involves substituting u = Tanx and du = Sec^2x dx into the original function.
Yes, the integration of (Tanx)^2(Secx) can be checked by differentiating the antiderivative that was found. The result should be equal to the original function, (Tanx)^2(Secx).