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Beliebt Rechnen >

integral from 0 to x of sqrt(1+x^2)

Lösung

\int_{0}^{x} 1 + x^{2} d x

Lösung

\frac{x x ^{2} + 1 + ln x + x ^{2} + 1}{2}

Schritte zur Lösung

\int_{0}^{x} 1 + x^{2} d x

Trigonometrische Substitution anwenden

= \int_{0}^{a r c t a n (x)} sec^{3} (u) d u

Wende integrale Reduktion an

= [\frac{sec ^{2} ( u ) sin ( u )}{2}]_{0}^{a r c t a n (x)} + \frac{1}{2} \cdot \int_{0}^{a r c t a n (x)} sec (u) d u

\int_{0}^{a r c t a n (x)} sec (u) d u = ln x + x^{2} + 1

= [\frac{sec ^{2} ( u ) sin ( u )}{2}]_{0}^{a r c t a n (x)} + \frac{1}{2} ln x + x^{2} + 1

Vereinfache

[\frac{sec ^{2} ( u ) sin ( u )}{2}]_{0}^{a r c t a n (x)} + \frac{1}{2} ln x + x^{2} + 1 : [\frac{1}{2} sec (u) tan (u)]_{0}^{a r c t a n (x)} + \frac{1}{2} ln x + x^{2} + 1

= [\frac{1}{2} sec (u) tan (u)]_{0}^{a r c t a n (x)} + \frac{1}{2} ln x + x^{2} + 1

Berechne die Grenzen:

\frac{1}{2} x x^{2} + 1

= \frac{1}{2} x x^{2} + 1 + \frac{1}{2} ln x + x^{2} + 1

Vereinfache

= \frac{x x ^{2} + 1 + ln x + x ^{2} + 1}{2}

Beliebte Beispiele

(\partial)/(\partial y)(x^2y+y^2z+xz^2)

derivative f(x)=(6x-1)/(x^3)

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integral from 0 to 3 of 1/(x-2)

fläche x,2xsqrt(81-x^2)