Question

An integration problem. (3/( x^3 + 3))dx Should I use integration by parts? Really confused.

Answer 1

please check if statement is correct.

Answer 2

partial fraction decomp?

Answer 3

To do partial fraction you have to factor the denominator.

Answer 4

sum of cubes

Answer 5

Try that then.

Answer 6

\[x ^{3}+3=\left( x+3^{\frac{ 1 }{ 3 }} \right)\left( x ^{2}+3^{\frac{ 1 }{ 3 }}x+3^{\frac{ 2 }{3 }} \right)\]

Answer 7

\[\frac{ 1 }{x ^{3}+3 }=\frac{ A }{x+3^{\frac{ 1 }{ 3 }} }+\frac{ Bx+C }{x ^{2}+3^{\frac{ 1 }{3 }}x+3^{\frac{ 2 }{3 }} }\]
cross multiply and compare terms with like powers of x