Question

( 2x(x2+1)4dx calcular la integral
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Answer 1

Respuesta:

∫ (2x(x^2+1))×4 dx = 2x^4+4x^2

∫ (2x(x^2+1))×4 dx

= ∫ (2x^3+2x)4 dx

= ∫ (8x^3+8x) dx

= ∫ 8(x^3+x) dx

= 8× ∫ (x^3+x)dx

∫ (x^3+x)dx

= ∫ (x^3)dx+ ∫ (x) dx

=( x^((3)+1)/((3)+1))+((x)^((1)+1)/(1+1))

= ( x^4/4)+(x^2/2)

= 2(x^4)+4(x^2)/(2×4) = (2x^4+4x^2)/8

Por lo que :

8× ∫ (x^3+x)dx

= 8 × ((2x^4+4x^2)/8)

= (16x^4+32x^2)/8

= 16x^4/8+32x^2/8

= 2x^4+4x^2

Explicación paso a paso: