Question #2e468

1 Answer
A08
Mar 28, 2017

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.

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