$y$ $\frac{\mathrm{d}y}{\mathrm{d}x}$ $\int \!y\, \mathrm{d}x$ (+ constant) sin $x$ cos $x$ $-$cos $x$ cos $x$ $-$sin $x$ sin $x$ tan $x$ sec$^2 x$ ln$($sec $x)$ arcsin $x$ $\frac{1}{\sqrt{1\:-\:x^2}}$ $x$ arcsin $x + \sqrt{1 - x^2}$ arccos $x$ $-\frac{1}{\sqrt{1\:-\:x^2}}$ $x$ arccos $x - \sqrt{1\:-\:x^2}$ arctan $x$ $\frac{1}{1\:+\:x^2}$ $x$ arctan $x - \frac{1}{2}$ln $(x^2 + 1)$ sec $x$ sec $x$ tan $x$ ln$\mid$sec $+$ tan $x \mid,$ ln$\mid$tan$(\frac{1}{2}x + \frac{1}{4}\pi)\mid$ csc $x$ $-$csc $x$ cot $x$ $-$ln$\mid$csc $x +$ cot $x\mid,$ ln$\mid$tan $\frac{1}{2}x\mid$ cot $x$ $-$csc$^2 x$ ln$\mid$sin $x\mid$ arcsec $x$ $\frac{1}{x^2\sqrt{1\:-\:\frac{1}{x^2}}}$ $x$ arcsec $x - \frac{\sqrt{1\:-\:\frac{1}{x^2}}\:x \ln{\sqrt{x^2\:-\:1}\:+\:x}}{\sqrt{x^2\:-\:1}}$ arccsc $x$ $-\frac{1}{x^2\sqrt{1\:-\:\frac{1}{x^2}}}$ $x$ arccsc $x + \frac{\sqrt{1\:-\:\frac{1}{x^2}}\:x \ln{\sqrt{x^2\:-\:1}\:+\:x}}{\sqrt{x^2\:-\:1}}$ arccot $x$ $\frac{1}{x^2\:+\:1}$ $\frac{1}{2}$ln $(x^2 + 1) + x$ arccot $x$