Math Formulas Search

1.

Multiplication rule

$a^m \cdot a^n=a^{m+n}$

2.

Zero exponent

$a^0=1$

3.

Division Rule

$\dfrac{a^m}{a^n}=a^{m-n}$

4.

Power of power rule

$\left(a^n\right)^m=a^{nm}$

5.

Negative exponent

$a^{-n}=\dfrac{1}{a^n}$

6.

Negative exponent of a fraction

$\left(\dfrac{a}{b}\right)^{-n} = \left(\dfrac{b}{a}\right)^n$

7.

Power of a product

$\left(ab\right)^n=a^n b^n$

8.

Power of a fraction

$\left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}$

9.

$ \int a^x dx = \dfrac{a^x}{\ln a} + C $

10.

$ \int e^{ax} dx = \dfrac{e^{ax}}{a}+C$

11.

$\int e^{ax} \sin bx dx = \dfrac{a\sin bx - b \cos bx}{a^2+b^2} e^{ax} + C $

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