Whakaoti i te ∫ (from -9 to 45) of 5x+8585+68*{(e)^15 wrt x

$$\int_{ -9 }^{ 45 } 5x+8585+68 \times {(e)^{ 15 }} d x$$

Aromātai

$$3672e^{15}+468450\approx 12004300241.717580795$$

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int 5x+8585+68e^{15}\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 5x\mathrm{d}x+\int 8585\mathrm{d}x+\int 68e^{15}\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$5\int x\mathrm{d}x+\int 8585\mathrm{d}x+68\int e^{15}\mathrm{d}x$$

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 5 ki te \frac{x^{2}}{2}.

$$\frac{5x^{2}}{2}+\int 8585\mathrm{d}x+68\int e^{15}\mathrm{d}x$$

Kimihia te tau tōpū o 8585 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$\frac{5x^{2}}{2}+8585x+68\int e^{15}\mathrm{d}x$$

Kimihia te tau tōpū o e^{15} mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$\frac{5x^{2}}{2}+8585x+68e^{15}x$$

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.

$$\frac{5}{2}\times 45^{2}+8585\times 45+68e^{15}\times 45-\left(\frac{5}{2}\left(-9\right)^{2}+8585\left(-9\right)+68e^{15}\left(-9\right)\right)$$

Whakarūnātia.

$$468450+3672e^{15}$$