calculus-integrals.tex

"\int x^n dx = \frac{1}{n + 1} x^{n + 1} + C" true
"\int \frac{1}{x} dx = \ln|x| + C" true
"\int c dx = c x + C" true
"\int x dx = \frac{1}{2} x^2 + C" true
"\int x^2 dx = \frac{1}{3} x^3 + C" true
"\int \frac{1}{x^2} dx = - \frac{1}{x} + C" true
"\int \sqrt{x} dx = \frac{2}{3} x \sqrt{x} + C" true
"\int \frac{1}{\sqrt{x}} dx = 2 \sqrt{x} + C" true
"\int \frac{1}{1 + x^2} dx = \arctan(x) + C" true
"\int \frac{1}{\sqrt{1 - x^2}} dx = \arcsin(x) + C" true
"\int \ln(x) dx = x \ln(x) - x + C" true
"\int x^n \ln(x) dx = \frac{x^{n + 1}}{n + 1} \ln(x) - \frac{x^{n + 1}}{(n + 1)^2} + C" true
"\int e^x dx = e^x + C" true
"\int b^x dx = \frac{1}{\ln(b)} b^x" true
"\int \sinh(x) dx = \cosh(x) + C" true
"\int \cosh(x) dx = \sinh(x) + C" true
"\int \sin(x) dx = -\cos(x) + C" true
"\int \cos(x) dx = \sin(x) + C" true
"\int \tan(x) dx = \ln(|\sec(x)|) + C" true
"\int \sec(x) dx = \ln(|\tan(x) + \sec(x)|) + C" true
"\int \sin^2(x) dx = \frac{1}{2} \left( x - \sin(x) \cos(x) \right) + C" true
"\int \cos^2(x) dx = \frac{1}{2} \left( x + \sin(x) \cos(x) \right) + C" true
"\int \tan^2(x) dx = \tan(x) - x + C" true
"\int \sec^2(x) dx = \tan(x) + C" true