integral of (1/2 sec^2(x)+x)

Lösung

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

\frac{1}{2} tan (x) + \frac{x ^{2}}{2} + C

Schritte zur Lösung

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1}{2} sec^{2} (x) d x + \int x d x

\int \frac{1}{2} sec^{2} (x) d x = \frac{1}{2} tan (x)

\int x d x = \frac{x ^{2}}{2}

= \frac{1}{2} tan (x) + \frac{x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} tan (x) + \frac{x ^{2}}{2} + C

\int \frac{1}{2000} e^{- \frac{x}{2000}} d x

\int \frac{3 e ^{x}}{4 e ^{x} - 1} d x

\int - 10 - 5 x^{2} d x

\int tan^{4} (2 x) sec^{4} (2 x) d x

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