f^'(x)=x^2e^{x^2}

Lösung

f^{^{'}} (x) = x^{2} e^{x^{2}}

f (x) = \frac{1}{2} e^{x^{2}} x - \frac{π}{4} erfi (x) + c_{1}

Schritte zur Lösung

f^{'} (x) = x^{2} e^{x^{2}}

Wenn

f^{^{'}} (x) = g (x)

dann

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

f (x) = \int x^{2} e^{x^{2}} d x

\int x^{2} e^{x^{2}} d x = \frac{1}{2} e^{x^{2}} x - \frac{π}{4} erfi (x) + c_{1}

f (x) = \frac{1}{2} e^{x^{2}} x - \frac{π}{4} erfi (x) + c_{1}

t an g e n t \frac{3 x}{x + 1}

d er i v a t i v e 2 x^{2} - \frac{1}{16} ln (x)

y = 8 i n^{x} + c

t \to 0 + lim (arctan (\frac{1}{t}))

\int (4 cos (θ))^{2} d θ