Advanced Math Solutions – Integral Calculator, common functions

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