What is the integral of 1/(3+x^3) ?

The integral of 1/(3+x^3) is y/(3+x^3)+C

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integral of 1/(3+x^3)

\int \frac{1}{3 + x ^{3}} d y

\frac{y}{3 + x ^{3}} + C

Solution steps

\int \frac{1}{3 + x ^{3}} d y

Integral of a constant:

\int a d x = a x

= \frac{1}{3 + x ^{3}} y

Simplify

\frac{1}{3 + x ^{3}} y : \frac{y}{3 + x ^{3}}

= \frac{y}{3 + x ^{3}}

Add a constant to the solution

= \frac{y}{3 + x ^{3}} + C

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