Question

Question #2e468

Answer 1

Simplify step

`=int_1^2 1/4sqrt(1/x^8)x^2sqrt(16x^8+8x^4+1)cdot dx`
`=>int_1^2 sqrt(1/16)sqrt(1/x^8)sqrt(x^4)sqrt(16x^8+8x^4+1)cdot dx`
`=>int_1^2 sqrt(1/(16x^4))sqrt(16x^8+8x^4+1)cdot dx`
`=>int_1^2 sqrt((16x^8+8x^4+1)/(16x^4))cdot dx`
`=>int_1^2 sqrt(x^4+1/2+1/(16x^4))cdot dx`

Now we notice that
`(x^4+1/2+1/(16x^4))=(x^2+1/(4x^2))^2`
Hence integrand becomes
`+-int_1^2 (x^2+1/(4x^2))cdot dx`
`=>+-[int_1^2 x^2cdot dx+int_1^2 1/(4x^2)cdot dx]`
`=>+-[ x^3/3+(-1/(4x))]_1^2`
Constants of integration have been omitted as these are definite integrals.
`=>+-[ x^3/3-1/(4x)]_1^2`

Complete the remaining and post result.