Datrys ∫ x^2left(x^3+2x^2-5right) wrt x

$$\int{ { x }^{ 2 } \left( { x }^{ 3 } +2 { x }^{ 2 } -5 \right) }d x$$

Enrhifo

$$\frac{x^{6}}{6}+\frac{2x^{5}}{5}-\frac{5x^{3}}{3}+С$$

Camau Ateb

Defnyddio’r briodwedd ddosbarthu i luosi x^{2} â x^{3}+2x^{2}-5.

$$\int x^{5}+2x^{4}-5x^{2}\mathrm{d}x$$

Integreiddio'r swm fesul term.

$$\int x^{5}\mathrm{d}x+\int 2x^{4}\mathrm{d}x+\int -5x^{2}\mathrm{d}x$$

Ffactoreiddio allan y cysonyn ym mhob un o'r termau.

$$\int x^{5}\mathrm{d}x+2\int x^{4}\mathrm{d}x-5\int x^{2}\mathrm{d}x$$

Ers \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} ar gyfer k\neq -1, disodli \int x^{5}\mathrm{d}x gyda \frac{x^{6}}{6}.

$$\frac{x^{6}}{6}+2\int x^{4}\mathrm{d}x-5\int x^{2}\mathrm{d}x$$

Ers \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} ar gyfer k\neq -1, disodli \int x^{4}\mathrm{d}x gyda \frac{x^{5}}{5}. Lluoswch 2 â \frac{x^{5}}{5}.

$$\frac{x^{6}}{6}+\frac{2x^{5}}{5}-5\int x^{2}\mathrm{d}x$$

Ers \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} ar gyfer k\neq -1, disodli \int x^{2}\mathrm{d}x gyda \frac{x^{3}}{3}. Lluoswch -5 â \frac{x^{3}}{3}.

$$\frac{x^{6}}{6}+\frac{2x^{5}}{5}-\frac{5x^{3}}{3}$$

Os yw F\left(x\right) yn integryn amhendant o f\left(x\right), yna bydd F\left(x\right)+C yn rhoi’r set o holl integrynnau amhendant f\left(x\right). Felly, ychwanegwch gysonyn yr integryn C\in \mathrm{R} at y canlyniad.

$$\frac{x^{6}}{6}+\frac{2x^{5}}{5}-\frac{5x^{3}}{3}+С$$

Gwahaniaethu w.r.t. x

$$x^{2}\left(x^{3}+2x^{2}-5\right)$$