Basic anti-derivative rules for common functions: ∫xndx=n+1xn+1+C
The integrals of sin and cos are
x1 is defined for x<0, but lnx is not. Specifically:
So x1 is the derivative of lnx and of ln(−x).
However, we can simplify further. Recall the definition of the absolute value:
Hence, we have
Nice work completing Anti-Derivative Rules, here's a quick recap of what we covered:
Exercises checked off
Basic anti-derivative rules for common functions: ∫xndx=n+1xn+1+C
The integrals of sin and cos are
x1 is defined for x<0, but lnx is not. Specifically:
So x1 is the derivative of lnx and of ln(−x).
However, we can simplify further. Recall the definition of the absolute value:
Hence, we have
Nice work completing Anti-Derivative Rules, here's a quick recap of what we covered:
Exercises checked off