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\int 5\mathrm{d}x+\int 2x\mathrm{d}x+\int \frac{1}{x}\mathrm{d}x
Kōmitimititia te kīanga tapeke mā te kīanga.
\int 5\mathrm{d}x+2\int x\mathrm{d}x+\int \frac{1}{x}\mathrm{d}x
Whakatauwehea te pūmau i ēnei kīanga katoa.
5x+2\int x\mathrm{d}x+\int \frac{1}{x}\mathrm{d}x
Kimihia te tau tōpū o 5 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.
5x+x^{2}+\int \frac{1}{x}\mathrm{d}x
Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x\mathrm{d}x ki te \frac{x^{2}}{2}. Whakareatia 2 ki te \frac{x^{2}}{2}.
5x+x^{2}+\ln(|x|)
Whakamahia te \int \frac{1}{x}\mathrm{d}x=\ln(|x|) mai i te ripanga o ngā tau tōpū pātahi kia whakaputa i te huanga.
5x+x^{2}+\ln(|x|)+С
Mēnā ko F\left(x\right) he pārōnaki kōaro o f\left(x\right), kāti ko te huinga o ngā pārōnaki kōaro katoa o f\left(x\right) ka whakaaturia e F\left(x\right)+C. Nō reira, me tāpiri te pūmau o te whakatōpūtanga C\in \mathrm{R} ki te otinga.