task/29858232
1. ∫dx /(1+9x²) = (1/3) ∫ 1 / ( 1+(3x)² ) d(3x) = (1/3)*arctg(3x) + C.
2. ∫(x⁴ -3x +1)dx =∫x⁴dx -∫3xdx +∫dx =∫x⁴dx -3∫xdx +∫dx = x⁵/5-3x²/2 +x +C.
3. ∫x²/(1+x⁶) dx =( 1/3)* ∫ 1/ (1+(x³)² ) d(x³) = ( 1/3)arctg(x³)+ C.
5. ∫ln(1+x²)dx =|| по частям || = xln(1+x²) - ∫xd( ln(1+x²) ) = xln(1+x²) -∫2x²/(1+x²)dx =xln(1+x²)-∫(2-2/(1+x²)dx = xln(1+x²) - 2x +2arctgx+ C .