\( \int x^n \, dx = \frac{x^{n+1}}{n+1} + c \)
\( \int e^x \, dx = e^x + c \)
\( \int \frac{1}{x} \, dx = \ln |x| + c \)
\(\int cos \, x \, dx = sin \, x + c\)
\(\int sin \, x \, dx = -cos \, x + c\)
\(\int sec^2 \, x \, dx = tan \, x + c\)
\(\int cosec \, x \, cot \, x \, dx = -cosec \, x + c\)
\(\int cosec^2 \, x \, dx = -cot \, x + c\)
\(\int sec \, x \,tan \, x \, dx = sec \, x + c\)
\(\int tan \, x \, dx = \ln|sec \, x| + c\)
\(\int sec \, x \, dx = \ln |sec \, x \, + \, tan \, x| + c\)
\(\int cot \, x \, dx = \ln |sin \, x| + c\)
\(\int cosec \, x \, dx = -\ln|cosec \, x + cot \, x|+c\)
\( \int \frac{1}{\sqrt{1-x^2}} \, dx = arcsin \, x + c \)
\( \int \frac{1}{\sqrt{a^2-x^2}} \, dx = arcsin \, \left(\frac{x}{a}\right) + c \)
\( \int -\frac{1}{\sqrt{1-x^2}} \, dx = arccos \, x + c \)
\( \int -\frac{1}{\sqrt{a^2-x^2}} \, dx = arccos \, \left(\frac{x}{a}\right) + c \)
\( \int \frac{1}{1+x^2} \, dx = arctan \, x + c \)
\( \int \frac{1}{a^2+x^2} \, dx = \frac{1}{a}arctan \, \left(\frac{x}{a}\right) + c \)
\( \int sinh \, x = cosh \, x +c \)
\( \int cosh \, x = sinh \, x +c \)
\( \int tanh \, x = ln|cosh \, x | +c \)
\( \int \frac{1}{\sqrt{x^2+1}} \, = arsinh \, x + c \)
\( \int \frac{1}{\sqrt{x^2+a^2}} \, = arsinh \, \frac{x}{a} + c \)
\( \int \frac{1}{\sqrt{x^2-1}} \, = arcosh \, x + c \)
\( \int \frac{1}{\sqrt{x^2-a^2}} \, = arcosh \, \frac{x}{a} + c \)
\( \int \frac{1}{1-x^2} \, = artanh \, x + c \)