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521.
Height of a segment
$h= r-\dfrac{1}{2}\sqrt{4r^2-a^2}, h < r $
522.
Segment area - verison 1
$ S = \dfrac{1}{2} \left(s r - a(r-h)\right)^2$
Area
Circle
Segment
523.
Segment area - verison 2
$ S = \dfrac{r^2}{2} \left(\dfrac{\alpha\pi}{180\degree} - \sin\alpha\right)$
Area
Circle
Segment
524.
Segment area - version 3
$S = \dfrac{r^2}{2}\left(x-\sin x \right)$
525.
$\int e^x dx = e^x + C$
E
Indefinite Integral
526.
$ \int a^x dx = \dfrac{a^x}{\ln a} + C $
Exponents
Indefinite Integral
527.
$ \int e^{ax} dx = \dfrac{e^{ax}}{a}+C$
Exponents
Indefinite Integral
528.
$ \int x e^{ax}dx = \dfrac{e^{ax}}{a^2}(ax-1)+C $
E
Indefinite Integral
529.
$ \int \ln x dx = x\ln x - x + C$
Indefinite Integral
Logarithm
530.
$ \int \dfrac{dx}{x\ln x} = \ln|\ln x| + C $
Indefinite Integral
Logarithm
531.
$ \int x \ln x dx = x^2 \left[\dfrac{\ln x}{2}-\dfrac{1}{4}\right] + C $
Indefinite Integral
Logarithm
532.
$ \int x^n \ln x dx = x^{n+1} \left[\dfrac{\ln x}{n+1}-\dfrac{1}{(n+1)^2}\right] + C $
Indefinite Integral
Logarithm
533.
$\int e^{ax} \sin bx dx = \dfrac{a\sin bx - b \cos bx}{a^2+b^2} e^{ax} + C $
E
Exponents
Indefinite Integral
Trigonometry
534.
$\int e^{ax} \cos bx dx = \dfrac{a\cos bx - b \sin bx}{a^2+b^2} e^{ax} + C $
E
Indefinite Integral
Trigonometry
535.
$ \int \sinh x dx = \cosh x + C$
Hyperbolic fun
Indefinite Integral
536.
$ \int \cosh x dx = \sinh x + C $
Hyperbolic fun
Indefinite Integral
537.
$ \tanh x dx = \ln \cosh x + C$
Hyperbolic fun
Indefinite Integral
538.
$ \int \coth x dx = \ln|\sinh x| + C $
Hyperbolic fun
Indefinite Integral
539.
$ \int \text{sech}^2 x dx = \tanh x + C $
Hyperbolic fun
Indefinite Integral
540.
$ $ \int \text{csch}^2 x dx = -\coth x + C $ $
Hyperbolic fun
Indefinite Integral

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