Question

assunto : integral diferenial II, ( mat: Antiderivadas )
encontre o valor de f (x2+4x5 -6)dx

Answer 1

Olá,

$\sf \: \int \: ( {x}^{2} + 4 {x}^{5} - 6 )\: dx \\ = \sf \: \int \: {x}^{2} \: dx + \sf \: \int \: 4 {x}^{5} \: dx - \sf \: \int \: 6 \: dx \\ \sf \: = \frac{ {x}^{2 + 1} }{2 + 1} + 4. \: \frac{ {x}^{5 + 1} }{5 + 1} - 6x + k \\ \sf \: = \frac{ {x}^{3} }{3} + \frac{4 {x}^{6} }{6} - 6x + k \\ \sf = \frac{ 1 }{3} {x}^{3} + \frac{4}{6} {x}^{6} - 6x + k$