integral from 0 to x of y/(1+y^4)

Lösung

\int_{0}^{x} \frac{y}{1 + y ^{4}} d y

\frac{1}{2} arctan (x^{2})

Schritte zur Lösung

\int_{0}^{x} \frac{y}{1 + y ^{4}} d y

Berechne das unbestimmte Integral:

\int \frac{y}{1 + y ^{4}} d y = \frac{1}{2} arctan (y^{2}) + C

Berechne die Grenzen:

\int_{0}^{x} \frac{y}{1 + y ^{4}} d y = \frac{1}{2} arctan (x^{2}) - 0

= \frac{1}{2} arctan (x^{2}) - 0

Vereinfache

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

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