Basic Integrals
- ∫ k dx = kx + C
- ∫ x^a dx = (x^(a+1))/(a+1) + C
- ∫ 1/x dx = ln|x| + C
- ∫ e^x dx = e^x + C
- ∫ a^x dx = (a^x)/ln(a) + C
- ∫ ln(x) dx = xln(x) - x + C
- ∫ logbase(a)(x) dx = xlogbase(a)(x) - x/ln(a) + C
- ∫ sin(x) dx = -cos(x) + C
- ∫ cos(x) dx = sin(x) + C
- ∫ tan(x) dx = -ln|cos(x)| + C = ln|sec(x)| + C
- ∫ cot(x) dx = ln|sin(x)| + C
- ∫ sec(x) dx = ln|sec(x) + tan(x)| + C
- ∫ csc(x) dx = ln|csc(x) - cot(x)| + C
- ∫ arcsin(x) dx = x arcsin(x) + √(1-x²| + C
- ∫ arccos(x) dx = x arccos(x) - √(1-x²| + C
- ∫ arctan(x) dx = x arctan(x) - ½ln|1+x²! + C
- ∫ arccot(x) dx = x arccot(x) + ½ln|1+x²! + C
- ∫ arcsec(x) dx = x arcsec(x) - arccosh(x) + C
- ∫ arccsc(x) dx = x arccsc(x) + arccosh(x) + C
- ∫ sinh(x) dx = cosh(x) + C
- ∫ cosh(x) dx = sinh(x) + C
- ∫ tanh(x) dx = ln|cosh(x)! + C
- ∫ csch(x) dx = ln|tanh(x/2)! + C
- ∫ sech(x) dx = arcsin(tanh(x/2)) + C
- ∫ coth(x) dx = ln(sinh(x)) + C
- ∫ arcsinh(x) dx = x arcsinh(x) - √(x²+1) + C
- ∫ arccosh(x) dx = x arccosh(x) - √(x²-1) + C
- ∫ arctanh(x) dx = x arctanh(x) + ½ln(1-x²) + C
- ∫ arccsch(x) dx = x arccsch(x) + ln[x(√(1+(1/x²))+1)]
- ∫ arcsech(x) dx = x arcsech(x) - arctan((x/(x-1))*√(1-x)/(1+x))
- ∫ arccoth(x) dx = x arccoth(x) + ½ln(x²-1) + C