Antiderivative of sec^2x
To find the antiderivative of sec^2x, we can use the power rule for integration
To find the antiderivative of sec^2x, we can use the power rule for integration.
The power rule states that the antiderivative of x^n with respect to x is (x^(n+1))/(n+1) + C, where C is the constant of integration.
In the case of sec^2x, we can rewrite it as (1/cos^2x). Using the definition of secant (sec(x) = 1/cos(x)), we have sec^2x = (1/cos^2x) = (sec(x))^2.
So, we can now rewrite the integral as the following:
∫sec^2x dx = ∫(sec(x))^2 dx.
Using the power rule, we add 1 to the exponent and divide by the new exponent, which is 2 + 1 = 3:
∫(sec(x))^2 dx = (1/3)(sec(x))^3 + C,
where C is the constant of integration.
Therefore, the antiderivative of sec^2x is (1/3)(sec(x))^3 + C.
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