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Question Number 94735 by student work last updated on 20/May/20

$$\int \frac{2\mathrm{t}}{(1+{\mathrm{t}}^4)(1+\mathrm{t})}\mathrm{dt}=?$$

Commented by student work last updated on 20/May/20

$$\mathrm{who}\mathrm{can}\mathrm{another}?$$

Commented by student work last updated on 20/May/20

$$\mathrm{who}\mathrm{can}\mathrm{solve}\mathrm{describly}?$$

Commented by MJS last updated on 20/May/20

$$\mathrm{are}\mathrm{you}\mathrm{able}\mathrm{to}\mathrm{decompose}?\mathrm{I}\mathrm{gave}\mathrm{you}$$$$\mathrm{enough}\mathrm{hints}.\mathrm{if}\mathrm{you}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{know}\mathrm{decomposition}$$$$\mathrm{start}\mathrm{with}\mathrm{some}\mathrm{easier}\mathrm{examples}.$$$${\mathrm{I}}^{\prime }\mathrm{m}\mathrm{tired}\mathrm{of}\mathrm{typing}\mathrm{obvious}\mathrm{things}.$$

Commented by student work last updated on 20/May/20

$$\mathrm{why}\mathrm{you}\mathrm{not}\mathrm{solve}?$$

Commented by MJS last updated on 20/May/20

$$\mathrm{I}\mathrm{solved}\mathrm{it}.\mathrm{Question}94574$$$$\mathrm{I}\mathrm{decomposed}\mathrm{it}\mathrm{in}2\mathrm{steps}.\mathrm{what}\mathrm{else}\mathrm{do}\mathrm{you}$$$$\mathrm{want}?$$

Commented by Tony Lin last updated on 21/May/20

$$\int \frac{2t}{(1+t^4)(1+t)}dt$$$$=\int \frac{t^3-t^2+t+1}{1+t^4}dt-\int \frac{1}{1+t}dt$$$$=\frac{1}{2\sqrt{2}}(\int \frac{(\sqrt{2}+2)t+\sqrt{2}}{t^2+\sqrt{2}t+1}dt+\int \frac{(\sqrt{2}-2)t+\sqrt{2}}{t^2-\sqrt{2}t+1}dt)-\int \frac{1}{1+t}dt$$$$nowitiseasytosolve$$$$itcanbeexpressedbylnandarctan$$

Commented by student work last updated on 21/May/20

$$\mathrm{explain}\mathrm{me}$$

Commented by MJS last updated on 21/May/20

$$\mathrm{Sir}\mathrm{Tony}\mathrm{Lin},\mathrm{this}\mathrm{is}\mathrm{exactly}\mathrm{what}\mathrm{I}\mathrm{answered}$$$$\mathrm{to}\mathrm{the}\mathrm{original}\mathrm{question}$$

Commented by MJS last updated on 21/May/20

$$\mathrm{Sir}\mathrm{student}\mathrm{work},\mathrm{if}\mathrm{you}\mathrm{cannot}\mathrm{solve}\mathrm{it}\mathrm{from}$$$$\mathrm{there},\mathrm{better}\mathrm{start}\mathrm{learning}\mathrm{basic}\mathrm{integrals}.$$$${\mathrm{there}}^{\prime }\mathrm{s}\mathrm{no}\mathrm{use}\mathrm{solving}\mathrm{problems}\mathrm{like}\mathrm{this}\mathrm{one}$$$$\mathrm{for}\mathrm{you}\mathrm{if}\mathrm{you}\mathrm{cannot}\mathrm{understand}\mathrm{each}\mathrm{simple}$$$$\mathrm{step}.$$

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