f dx/ sqrt (a² - x²) = arcsin x/|a| + c

f dx/ sqrt (x² + a) = ln | x + sqrt (x² + a) | + c

f sqrt (a² - x²) dx = a²/2 arcsin x/|a| + x/2 sqrt (a² - x²) + c

f sqrt (x² + a) dx = (1/2)*x sqrt (x² + a) + (1/2)*a ln |x + sqrt (x² + a) | + c

f sinⁿxdx = - 1/n sin^n-1 xcosx + n-1/n f sin^n-2xdx

fcos ⁿxdx = 1/n cos^n-1xsinx + n-1/n f cos^n-2xdx

sinx,cosx.../tgx,sinx...

T = tg x/2

T = tg x/2 => x =2arctgt => dx = 2dt/ 1 + t²

sinx = 2t/ 1+t² , cosx = 1 - t² / 1 + t² , tgx = 2t/1-t² , ctgx = 1- t² / 2t

sin²x, cos²x, sinxcosx

t=tgx x=arctgt dx=1/1+t²dt sin²x=t²/1+t² cos²t=1/1+t²

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