All Maths Formulas

Algebra

\int \infty 0 d x x 2 + a 2 = π 2 a

$\int^\infty_0 \frac{dx}{x^2+a^2} = \frac{\pi}{2a}$

\int \infty 0 x p - 1 d x 1 + x = π sin ( p π ), 0 < p < 1

$\int^\infty_0 \frac{x^{p-1}\,dx}{1+x} = \frac{\pi}{\sin (p\pi)} , ~ 0 < p < 1$

\int \infty 0 x m x n + a n = π a m + 1 - n n sin [ ( m + 1 ) π / n ], 0 < m + 1 < n

$\int^\infty_0 \frac{x^m}{x^n + a^n} = \frac{\pi a^{m + 1 -n}}{n\,\sin[(m+1)\pi/n]}, ~0 < m + 1 < n$

\int a 0 d x a 2 - x 2 - - - - - - \sqrt = π 2

$\int^a_0 \frac{dx}{\sqrt{a^2 - x^2}} = \frac{\pi}{2}$

\int a 0 a 2 - x 2 - - - - - - \sqrt d x = π a 2 4

$\int^a_0 \sqrt{a^2 - x^2}\,dx = \frac{\pi\,a^2}{4}$

\int a 0 x m (a n - x n) p d x = a m + 1 + n p Γ [ ( m + 1 ) / n ] Γ ( p + 1 ) n Γ [ ( m + 1 ) / n + p + 1 ]

$\int^a_0 x^m \left(a^n - x^n\right)^p\,dx = \frac{a^{m+1+np}~\Gamma[(m+1)/n]~\Gamma(p+1) }{n\,\Gamma[(m+1)/n + p +1]}$

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