integral of 1/(xsqrt(225x^2-225))

Lösung

\int \frac{1}{x 225 x ^{2} - 225} d x

\frac{1}{15} arctan (x^{2} - 1) + C

Schritte zur Lösung

\int \frac{1}{x 225 x ^{2} - 225} d x

Wende die partielle Integration an

= \frac{1}{15 x ^{2} - 1} - \int - \frac{2 x ^{2} - 1}{15 x ( x ^{2} - 1 ) x ^{2} - 1} d x

\int - \frac{2 x ^{2} - 1}{15 x ( x ^{2} - 1 ) x ^{2} - 1} d x = - \frac{1}{15} (- \frac{1}{x ^{2} - 1} + arctan (x^{2} - 1))

= \frac{1}{15 x ^{2} - 1} - (- \frac{1}{15} (- \frac{1}{x ^{2} - 1} + arctan (x^{2} - 1)))

Vereinfache

\frac{1}{15 x ^{2} - 1} - (- \frac{1}{15} (- \frac{1}{x ^{2} - 1} + arctan (x^{2} - 1))) : \frac{1}{15} arctan (x^{2} - 1)

= \frac{1}{15} arctan (x^{2} - 1)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{15} arctan (x^{2} - 1) + C

\int \frac{x}{( 7 ^{2} - x ^{2} ) ^{3}} d x

\frac{\partial}{\partial x} (e^{y} - 3)

\frac{d}{d x} ((2 x^{2} - 5)^{- 15})

t an g e n t f (x) = (x - 5)^{2}, at x = 1

\int_{0}^{l n (4)} 3 (4 - x e^{x}) d x