Whakaoti i te ∫ (x^2/2-2/x^2) wrt x=x^3/6+2/x+c

$$\int ( \frac { x ^ { 2 } } { 2 } - \frac { 2 } { x ^ { 2 } } ) d x = \frac { x ^ { 3 } } { 6 } + \frac { 2 } { x } + c$$

Whakaoti mō c

$$c=С$$

$$x\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 6x, arā, te tauraro pātahi he tino iti rawa te kitea o 6,x.

$$6x\int \frac{x^{2}}{2}-\frac{2}{x^{2}}\mathrm{d}x=xx^{3}+6\times 2+6xc$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 1 me te 3 kia riro ai te 4.

$$6x\int \frac{x^{2}}{2}-\frac{2}{x^{2}}\mathrm{d}x=x^{4}+6\times 2+6xc$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 2 me x^{2} ko 2x^{2}. Whakareatia \frac{x^{2}}{2} ki te \frac{x^{2}}{x^{2}}. Whakareatia \frac{2}{x^{2}} ki te \frac{2}{2}.

$$6x\int \frac{x^{2}x^{2}}{2x^{2}}-\frac{2\times 2}{2x^{2}}\mathrm{d}x=x^{4}+6\times 2+6xc$$

Tā te mea he rite te tauraro o \frac{x^{2}x^{2}}{2x^{2}} me \frac{2\times 2}{2x^{2}}, me tango rāua mā te tango i ō raua taurunga.

$$6x\int \frac{x^{2}x^{2}-2\times 2}{2x^{2}}\mathrm{d}x=x^{4}+6\times 2+6xc$$

Mahia ngā whakarea i roto o x^{2}x^{2}-2\times 2.

$$6x\int \frac{x^{4}-4}{2x^{2}}\mathrm{d}x=x^{4}+6\times 2+6xc$$

Whakareatia te 6 ki te 2, ka 12.

$$6x\int \frac{x^{4}-4}{2x^{2}}\mathrm{d}x=x^{4}+12+6xc$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{4}+12+6xc=6x\int \frac{x^{4}-4}{2x^{2}}\mathrm{d}x$$

Tangohia te x^{4} mai i ngā taha e rua.

$$12+6xc=6x\int \frac{x^{4}-4}{2x^{2}}\mathrm{d}x-x^{4}$$

Tangohia te 12 mai i ngā taha e rua.

$$6xc=6x\int \frac{x^{4}-4}{2x^{2}}\mathrm{d}x-x^{4}-12$$

He hanga arowhānui tō te whārite.

$$6xc=Сx$$

Whakawehea ngā taha e rua ki te 6x.

$$\frac{6xc}{6x}=\frac{Сx}{6x}$$

Mā te whakawehe ki te 6x ka wetekia te whakareanga ki te 6x.

$$c=\frac{Сx}{6x}$$

Whakawehe Сx ki te 6x.

$$c=\frac{С}{6}$$

Whakaoti mō x

$$x\neq 0$$

$$c=С\text{ and }x\neq 0$$