Calculus • Step-by-Step

Integral of sec²(x) dx with Steps

Find the integral of sec²(x) dx step by step. Reverses the derivative of tan(x) to yield tan(x) + C.

Problem Statement

\int \sec^2(x) \, dx

Final Result

F(x) = \mathrm{tan}\left(x\right) + C

Formula Required: Secant Squared Integration

Because d/dx[tan(x)] = sec²(x), the integral of sec²(x) is tan(x).

\int \sec^2(x) \, dx = \tan(x) + C

2 Steps

Set up the indefinite integral with respect to variable $x$.

\int \left( \mathrm{sec}\left(x\right)^{2} \right) \, dx

Apply the Power Rule for Integration to find the antiderivative.

F(x) = \mathrm{tan}\left(x\right)

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The integral of sec²(x) is tan(x) + C.