Question

Evaluate the indefinite integral. (use c for the constant of integration.) int (x**(7))/(1 + x**(16)) dx

Answer 1

`\displaystyle\int(x^7)/(1+x^(16))\,\mathrm dx`

Notice that
`x^(16)=(x^8)^2`, so let's make the substitution
`y=x^8`, so that
`\mathrm dy=8x^7\,\mathrm dx`. Then the above can be written as


`\displaystyle\frac18\int(\mathrm dy)/(1+y^2)=\frac18\tan^(-1)y+C=\frac18\tan^(-1)x^8+C`