Whakaoti i te ∫ [a^2-5a+6/a^2+7a+6:(2a+10/a+1-a-1)+1/a+3]*2a^2+5a-3/2a^2

$$\int [ \frac { a ^ { 2 } - 5 a + 6 } { a ^ { 2 } + 7 a + 6 } : ( \frac { 2 a + 10 } { a + 1 } - a - 1 ) + \frac { 1 } { a + 3 } ] \cdot \frac { 2 a ^ { 2 } + 5 a - 3 } { 2 a ^ { 2 } }$$

Aromātai

$$\frac{8ax-4x}{\left(a+6\right)a^{2}}+С$$

Ngā Upane Otinga

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia -a-1 ki te \frac{a+1}{a+1}.

$$\int \left(\frac{\frac{a^{2}-5a+6}{a^{2}+7a+6}}{\frac{2a+10}{a+1}+\frac{\left(-a-1\right)\left(a+1\right)}{a+1}}+\frac{1}{a+3}\right)\times \frac{2a^{2}+5a-3}{2a^{2}}\mathrm{d}x$$

Tā te mea he rite te tauraro o \frac{2a+10}{a+1} me \frac{\left(-a-1\right)\left(a+1\right)}{a+1}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\int \left(\frac{\frac{a^{2}-5a+6}{a^{2}+7a+6}}{\frac{2a+10+\left(-a-1\right)\left(a+1\right)}{a+1}}+\frac{1}{a+3}\right)\times \frac{2a^{2}+5a-3}{2a^{2}}\mathrm{d}x$$

Mahia ngā whakarea i roto o 2a+10+\left(-a-1\right)\left(a+1\right).

$$\int \left(\frac{\frac{a^{2}-5a+6}{a^{2}+7a+6}}{\frac{2a+10-a^{2}-a-a-1}{a+1}}+\frac{1}{a+3}\right)\times \frac{2a^{2}+5a-3}{2a^{2}}\mathrm{d}x$$

Whakakotahitia ngā kupu rite i 2a+10-a^{2}-a-a-1.

$$\int \left(\frac{\frac{a^{2}-5a+6}{a^{2}+7a+6}}{\frac{9-a^{2}}{a+1}}+\frac{1}{a+3}\right)\times \frac{2a^{2}+5a-3}{2a^{2}}\mathrm{d}x$$

Whakawehe \frac{a^{2}-5a+6}{a^{2}+7a+6} ki te \frac{9-a^{2}}{a+1} mā te whakarea \frac{a^{2}-5a+6}{a^{2}+7a+6} ki te tau huripoki o \frac{9-a^{2}}{a+1}.

$$\int \left(\frac{\left(a^{2}-5a+6\right)\left(a+1\right)}{\left(a^{2}+7a+6\right)\left(9-a^{2}\right)}+\frac{1}{a+3}\right)\times \frac{2a^{2}+5a-3}{2a^{2}}\mathrm{d}x$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{\left(a^{2}-5a+6\right)\left(a+1\right)}{\left(a^{2}+7a+6\right)\left(9-a^{2}\right)}.

$$\int \left(\frac{\left(a-3\right)\left(a-2\right)\left(a+1\right)}{\left(a-3\right)\left(-a-3\right)\left(a+1\right)\left(a+6\right)}+\frac{1}{a+3}\right)\times \frac{2a^{2}+5a-3}{2a^{2}}\mathrm{d}x$$

Me whakakore tahi te \left(a-3\right)\left(a+1\right) i te taurunga me te tauraro.

$$\int \left(\frac{a-2}{\left(-a-3\right)\left(a+6\right)}+\frac{1}{a+3}\right)\times \frac{2a^{2}+5a-3}{2a^{2}}\mathrm{d}x$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o \left(-a-3\right)\left(a+6\right) me a+3 ko \left(a+3\right)\left(a+6\right). Whakareatia \frac{a-2}{\left(-a-3\right)\left(a+6\right)} ki te \frac{-1}{-1}. Whakareatia \frac{1}{a+3} ki te \frac{a+6}{a+6}.

$$\int \left(\frac{-\left(a-2\right)}{\left(a+3\right)\left(a+6\right)}+\frac{a+6}{\left(a+3\right)\left(a+6\right)}\right)\times \frac{2a^{2}+5a-3}{2a^{2}}\mathrm{d}x$$

Tā te mea he rite te tauraro o \frac{-\left(a-2\right)}{\left(a+3\right)\left(a+6\right)} me \frac{a+6}{\left(a+3\right)\left(a+6\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\int \frac{-\left(a-2\right)+a+6}{\left(a+3\right)\left(a+6\right)}\times \frac{2a^{2}+5a-3}{2a^{2}}\mathrm{d}x$$

Mahia ngā whakarea i roto o -\left(a-2\right)+a+6.

$$\int \frac{-a+2+a+6}{\left(a+3\right)\left(a+6\right)}\times \frac{2a^{2}+5a-3}{2a^{2}}\mathrm{d}x$$

Whakakotahitia ngā kupu rite i -a+2+a+6.

$$\int \frac{8}{\left(a+3\right)\left(a+6\right)}\times \frac{2a^{2}+5a-3}{2a^{2}}\mathrm{d}x$$

Me whakarea te \frac{8}{\left(a+3\right)\left(a+6\right)} ki te \frac{2a^{2}+5a-3}{2a^{2}} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\int \frac{8\left(2a^{2}+5a-3\right)}{\left(a+3\right)\left(a+6\right)\times 2a^{2}}\mathrm{d}x$$

Me whakakore tahi te 2 i te taurunga me te tauraro.

$$\int \frac{4\left(2a^{2}+5a-3\right)}{\left(a+3\right)\left(a+6\right)a^{2}}\mathrm{d}x$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{4\left(2a^{2}+5a-3\right)}{\left(a+3\right)\left(a+6\right)a^{2}}.

$$\int \frac{4\left(2a-1\right)\left(a+3\right)}{\left(a+3\right)\left(a+6\right)a^{2}}\mathrm{d}x$$

Me whakakore tahi te a+3 i te taurunga me te tauraro.

$$\int \frac{4\left(2a-1\right)}{\left(a+6\right)a^{2}}\mathrm{d}x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te 2a-1.

$$\int \frac{8a-4}{\left(a+6\right)a^{2}}\mathrm{d}x$$

Whakamahia te āhuatanga tohatoha hei whakarea te a+6 ki te a^{2}.

$$\int \frac{8a-4}{a^{3}+6a^{2}}\mathrm{d}x$$

Kimihia te tau tōpū o \frac{8a-4}{a^{3}+6a^{2}} mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$\frac{8a-4}{a^{3}+6a^{2}}x$$

Whakarūnātia.

$$\frac{\left(8a-4\right)x}{a^{3}+6a^{2}}$$

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.

$$\frac{\left(8a-4\right)x}{a^{3}+6a^{2}}+С$$

Kimi Pārōnaki e ai ki x

$$\frac{4\left(2a-1\right)}{\left(a+6\right)a^{2}}$$