In the previous post we covered the basic integration rules (
click here). Before we continue with more advanced techniques, we will cover some common integrals (reciprocal, exponential and trigonometric functions). You will be using the common integrals a lot, so get to know them well.
Reciprocal & Exponential:
\int\frac{1}{x}dx=\ln|x|+C
\int e^x dx=e^x+C
\int a^x dx=\frac{a^x}{\ln(a)}+C
Trigonometry:
\int\cos(x)dx=\sin(x)+C
\int\sin(x)dx=-\cos(x)+C
\int\sec^2(x)dx=\tan(x)+C
\int\csc^2(x)dx=-\cot(x)+C
The remaining trig functions can be integrated using advanced techniques, but that’s for later.
Let’s take a look at a few examples (we’re doing it slowly)
Starting with basic trigonometric functions (
click here):
Exponential function (
click here):
Here’s an example using the sum rule, power rule, and common integrals (
click here):
Still doing good.
Cheers,
Michal
