Question

Calcule as integrais indefinidas abaixo

∫(x^2+1)(x^3+3)^4 ???

Answer 1

Resposta:

∫(x^2+1)(x^3+3)^4 dx

(x^2+1)(x^3+3)⁴ = x¹⁴ +x¹²+12x¹¹+12x⁹+54x⁶+108x⁵+108x³+81x²+81

∫(x^2+1)(x^3+3)^4 dx = ∫ x¹⁴ +x¹²+12x¹¹+12x⁹+54x⁶+108x⁵+108x³+81x²+81 dx

x¹⁵/15+x¹³/13+12x¹¹/12+54x⁷/7+108x⁶/6+108x⁴/4+81x³/3+81x +constante

=x¹⁵/15+x¹³/13+x¹¹+54x⁷/7+18x⁶+27x⁴+27x³+81x +constante