Beregn ∫x⋅ex2 dx\int x \cdot e^{x^2}\,dx∫x⋅ex2dx ved substitusjon.
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La u=x2u = x^2u=x2, da du=2x dx⇒x dx=12du\displaystyle du = 2x\,dx \Rightarrow x\,dx = \frac{1}{2}dudu=2xdx⇒xdx=21du.
∫x⋅ex2 dx=12∫eu du=12eu+C=12ex2+C\displaystyle \int x \cdot e^{x^2}\,dx = \frac{1}{2}\int e^u\,du = \frac{1}{2}e^u + C = \frac{1}{2}e^{x^2} + C∫x⋅ex2dx=21∫eudu=21eu+C=21ex2+C.
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