Derivative Rule

Trigonometric Identities

Basics

<aside> 💡 Just like exponential and logarithmic function—or like the arc-trig and trig—We are finding the input before the derivation.

</aside>

• $\int 0dx=C$
• $\int k=kx+C$
• $\int [k\cdot f(x)] dx= k \int [f(x)]$
• $\int [f(x)+g(x)] dx= \int f(x) dx +\int g(x) dx$
• $\int x^n=\frac 1 {x+1} x^{n+1} +C, n\ne - 1$

• $\int \frac 1 xdx =\ln |x|+C$
• $\int e^xdx=e^x+C$

Remember that $\ln a$ is constant. Never try to cancel a variable term….

• $\int \csc x dx=-\ln |\csc x+\cot x|+C$

Trig

• $\int \cos x dx=\sin x+C$

• $\int \sec ^2x dx=\tan x+ C$

• $\int \sec x \tan x dx=\sec x+C$

• $\int \sin x dx=-\cos x+C$

• $\int \csc^2x dx=-\cot x+C$

• $\int \csc x \cot x dx= -\csc x +C$

• $\int \tan x = -\ln (\cos x)+C$. no

• $\int \cot xdx = \ln (\sin x)+C$

• $\int \sec x dx=\ln |\sec x+\tan x|+C$