integral of arctan(sqrt(\sqrt{x)-1})

Lösung

\int arctan (x - 1) d x

x arctan (x - 1) - \frac{1}{3} (x - 1)^{\frac{3}{2}} - x - 1 + C

Schritte zur Lösung

\int arctan (x - 1) d x

Wende die partielle Integration an

= x arctan (x - 1) - \int \frac{1}{4 x - 1} d x

\int \frac{1}{4 x - 1} d x = \frac{1}{3} (x - 1)^{\frac{3}{2}} + x - 1

= x arctan (x - 1) - (\frac{1}{3} (x - 1)^{\frac{3}{2}} + x - 1)

Vereinfache

= x arctan (x - 1) - \frac{1}{3} (x - 1)^{\frac{3}{2}} - x - 1

Füge eine Konstante zur Lösung hinzu

= x arctan (x - 1) - \frac{1}{3} (x - 1)^{\frac{3}{2}} - x - 1 + C

\int \frac{1}{( x ^{3} - 1 )} d x

\int \frac{2 x ^{2} - 1}{x ( x + 1 ) ^{3}} d x

\frac{d}{d x} (tan (1 - x))

\frac{\partial}{\partial x} (x^{2} + 10 x y + y^{2})

x \to 0 + lim (x \cdot (e^{\frac{1}{x}} - 1))