Integralni bajarishdan oldin biz qismni ajratishimiz va biroz soddalashtirishimiz kerak.

\[\int{{{t^3} - \frac{{{{\bf{e}}^{ - t}} - 4}}{{{{\bf{e}}^{ - t}}}}\,dt}} = \int{{{t^3} - \frac{{{{\bf{e}}^{ - t}}}}{{{{\bf{e}}^{ - t}}}} + \frac{4}{{{{\bf{e}}^{ - t}}}}\,dt}} = \int{{{t^3} - 1 + 4{{\bf{e}}^t}\,dt}}\]

Ikkinchi hadni bo'lishda minus belgisini to'g'ri taqsimlaganingizga ishonch hosil qiling va uchinchi hadning maxrajidagi ko'rsatkichni (integrandni ajratgandan so'ng) suratga ko'chirishni va \(t\) belgisini jarayonda "+" ga o'zgartirishni unutmang.

2-qadam

Hozirgi vaqtda integralni baholashdan boshqa hech narsa qilish kerak emas.

\[\int{{{t^3} - \frac{{{{\bf{e}}^{ - t}} - 4}}{{{{\bf{e}}^{ - t}}}}\,dt}} = \int{{{t^3} - 1 + 4{{\bf{e}}^t}\,dt}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{1}{4}{t^4} - t + 4{{\bf{e}}^t} + c}}\]