Podstawowe wzory rachunku całkowego

Zestawiamy podstawowe wzory rachunku całkowego:

• $\int$x^adx = ${\frac{{x^{a+1}}}{{a+1}}}$ + C, gdzie a $\neq$ - 1, x > 0,
• $\int$${\frac{{dx}}{{x}}}$ = ln| x| + C, gdzie x $\neq$ 0,
• $\int$e^xdx = e^x + C,
• $\int$a^xdx = ${\frac{{a^x}}{{\ln a}}}$ + C, gdzie a > 0, a $\neq$ 1,
• $\int$cosxdx = sinx + C,
• $\int$sinxdx = - cosx + C,
• $\int$${\frac{{dx}}{{cos^2 x}}}$ = tgx + C, gdzie cosx $\neq$ 0,
• $\int$${\frac{{dx}}{{sin^2 x}}}$ = - ctgx + C, gdzie sinx $\neq$ 0,
• $\int$${\frac{{dx}}{{\sqrt{1 - x^2}}}}$ = arcsinx + C = - arccosx + C', gdzie -1 < x < 1,
• $\int$${\frac{{dx}}{{x^2 + 1}}}$ = arctgx + C = - arctgx + C',
• $\int$sinhxdx = coshxdx + C,
• $\int$coshxdx = sinhxdx + C,
• $\int$${\frac{{dx}}{{cosh^2 x}}}$ = tghx + C,
• $\int$${\frac{{dx}}{{sinh^2 x}}}$ = - ctghx + C,
• $\int$${\frac{{dx}}{{\sqrt{1 + x^2}}}}$ = arsinhx + C = ln(x + $\sqrt{{x^2 + 1}}$) + C,
• $\int$${\frac{{dx}}{{\sqrt{x^2 - 1}}}}$ = arcoshx + C = ln| x + $\sqrt{{x^2 - 1}}$| + C, gdzie | x| > 1.