Angles are in radians; a 0. Use intervals where the integrand is defined. Integration reverses the following derivatives. ddxsin x=cos x x,dx=sin x+C ddxcos x=-sin x x,dx=-cos x+C ddxtan x=sec2x 2x,dx=tan x+C Linear arguments (ax+b), dx=- cos(ax+b)a+C (ax+b), dx= sin(ax+b)a+C 2(ax+b), dx= tan(ax+b)a+C Sine integrates to negative cosine. If a = 0, integrate the resulting constant when defined.

Angles are in radians; \(a\ne0\). Use intervals where the integrand is defined.

Integration reverses the following derivatives.

\(\dfrac{\mathrm{d}}{\mathrm{d}x}\sin x=\cos x\qquad\int\cos x\,\mathrm{d}x=\sin x+C\)

\(\dfrac{\mathrm{d}}{\mathrm{d}x}\cos x=-\sin x\qquad\int\sin x\,\mathrm{d}x=-\cos x+C\)

\(\dfrac{\mathrm{d}}{\mathrm{d}x}\tan x=\sec^2x\qquad\int\sec^2x\,\mathrm{d}x=\tan x+C\)

\(\int\sin(ax+b)\,\mathrm dx=-\dfrac{\cos(ax+b)}a+C\)

\(\int\cos(ax+b)\,\mathrm dx=\dfrac{\sin(ax+b)}a+C\)

\(\int\sec^2(ax+b)\,\mathrm dx=\dfrac{\tan(ax+b)}a+C\)

Sine integrates to negative cosine. If a = 0, integrate the resulting constant when defined.

Integration of Trigonometric Functions

Integration of Trigonometric Functions