Question

integrate x^2+1/(x^3+3x+7)^3 dx​

Answer 1

Answer:

Integration of

$\frac{ ({x}^{2} + 1)dx}{( {x}^{3} + 3x + 7) {}^{3} } =$

$let \: {x}^{3} + 3x + 7 = t \\( 3 {x}^{2} + 3)dx = dt \\ 3( {x}^{2} + 1)dx = dt$

replacing these assumptions, we get

$\frac{dt}{3 {t}^{3} } = \frac{1}{3} \frac{ {t}^{ - 3 + 1} }{ - 3 + 1} + c = - \frac{1}{6 {t}^{2} } + c$

replacing t,

Required integration =

$- \frac{1}{6( {x}^{3} + 3x + 7) {}^{2} } + c$

Ans.

Answer 2

Answer:

nice work in above solution. great