Santiago M. Book of Integrals. Exploring Species of Integrals...Techniques 2024

Textbook in PDF format

This is your integration bible!
The climb up Mt Calculus is an arduous one. You limit-gaze at the base of the mountain, cut away at derivatives, but now it’s time to put all your skills to the test. Book of Integrals Is my love letter to calculus and its anti derivatives. These curious little things have so much to unpack and will test your skillset. Come join me and explore certain methods needed to survive these beasts ! We will explore from the basics, the most common integrals seen in calculus, and we will uncover some fascinating methods that stump even the best of math nerds. But, most importantly, We’ll have some fun.
The Power Rule.
Trig, Exponentials and Logs.
U-sub Integration.
Manipulating the Root.
Special Trig integrals.
Completing the Square.
Trig Substitution.
Partial Fraction Decomposition.
Long Division then PFD.
Rational Root Theorem.
The P.U.N. Integral.
Ultra Violet Voodoo.
Ultra Violet Voodoo, but With a Ghost.
Ultra violet voodoo, but Move That shit to The Other Side.
Ultra Violet Voodoo, But With Tic-Tac-Toe.
Power Reducing Integrals.
The Wallis Integrals.
Sine-Cosine With Different Angles.
Weierstrass Substitution.
The radicals.
Area Under the Curve - The Beginning.
King’s Rule.
The S.E. - One Method.
More, Please.
A PFD Trick (sometimes).
Euler’s Formula.
Controversial Quad-Root Trick.
Demoivre and 1/(x^5+1).
Feynman Technique.
Taylor (no, not that Taylor) Expansion.
The Dilogarithm Function.
The Work Never Ends.
Answer Key