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Aromātai
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\int \frac{5}{\sqrt{x}}\mathrm{d}x
Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.
5\int \frac{1}{\sqrt{x}}\mathrm{d}x
Whakatauwehetia te pūmau mā te whakamahi i te \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.
10\sqrt{x}
Tuhia anō te \frac{1}{\sqrt{x}} hei x^{-\frac{1}{2}}. Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x^{-\frac{1}{2}}\mathrm{d}x ki te \frac{x^{\frac{1}{2}}}{\frac{1}{2}}. Whakarūnāhia me te tahuri mai i te āhua taupū ki te āhua pūtake.
10\times 5^{\frac{1}{2}}-10\times 2^{\frac{1}{2}}
Ko te tau tōpū tautuhi ko te pārōnaki kōaro o te kīanga i aromātaitia i te tepe tōrunga o te pāwhaitua, tangohia te pārōnaki kōaro i aromātaitia i te tepe tōraro o te pāwhaitua.
10\sqrt{5}-10\sqrt{2}
Whakarūnātia.