Integration

\tan x + C

The derivative of \( \tan x \) is \( \sec^2 x \), so the integral of \( \sec^2 x \) is \( \tan x + C \).

\log |x| + C

The integral of \( \frac{1}{x} \) is \( \log |x| + C \) for \( x \neq 0 \).

-\cos x + C

The derivative of \( -\cos x \) is \( \sin x \), so the integral of \( \sin x \) is \( -\cos x + C \).

\ x + C

The integral of 1 with respect to x is x plus a constant of integration.