Помогите, пожалуйста, найти интеграл
int t^8/(1 + t^2) dt
int t^8/(1 + t^2) dt =
= int (t^8 + t^6 - t^6 - t^4 + t^4 + t^2 - t^2 - 1 + 1)/(1 + t^2) dt =
= int (t^6 * (t^2 + 1) - t^4 * (t^2 + 1) + t^2 * (t^2 + 1) - (t^2 + 1) + 1)/(1 + t^2) dt =
= int t^6 dt - int t^4 dt + int t^2 dt - int dt + int dt/(1 + t^2) =
= 1/7 * t^7 - 1/5 * t^5 + 1/3 * t^3 - t + arctg t + C
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