∫ sec^2(x) dx
To find the integral of sec^2(x) dx, we can use a trigonometric identity
To find the integral of sec^2(x) dx, we can use a trigonometric identity. The identity states that the derivative of the tangent function is equal to the sec^2(x).
We can rewrite our integral as:
∫ sec^2(x) dx = ∫ 1/cos^2(x) dx
Using the trigonometric identity, we know that 1/cos^2(x) is equal to the derivative of the tangent function. Therefore, we can simplify our integral to:
∫ sec^2(x) dx = ∫ d(tan(x))
Now, we can integrate d(tan(x)), which is simply the derivative of tan(x):
∫ d(tan(x)) = tan(x) + C
Where C is the constant of integration.
Therefore, the integral of sec^2(x) dx is equal to tan(x) + C.
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