Integrate the following indefinite integral. ∫ dx /√8x+3 + √8x

1.	Integrate the following indefinite integral. ∫ dx /√8x+3 + √8x+1\(\int\frac{dx}{\sqrt{8x+3}+\sqrt{8x+1}}\)
Answer» \(\int\frac{dx}{\sqrt{8x+3}+\sqrt{8x+1}}\) = \(\int\frac{\sqrt{8x+3}-\sqrt{8x+1}}{(8x+3)-(8x+1)}dx\) = \(\int\frac{\sqrt{8x+3}-\sqrt{8x+1}}{2}dx\) = \(\frac12[\int\sqrt{8x+3}dx-\int\sqrt{8x+1}dx]\) = \(\frac12[\frac23\frac{(8x+3)^{3/2}}8-\frac23\frac{(8x+1)^{3/2}}8]+c\) = \(\frac12\times\frac23\times\frac18[(8x+3)^{3/2}-(8x+1)^{3/2}]+c\) = \(\frac1{24}[(8x+3)^{3/2}-(8x+1)^{3/2}]+c\)

Integrate the following indefinite integral. ∫ dx /√8x+3 + √8x+1\(\int\frac{dx}{\sqrt{8x+3}+\sqrt{8x+1}}\)

Answer»

\(\int\frac{dx}{\sqrt{8x+3}+\sqrt{8x+1}}\)

= \(\int\frac{\sqrt{8x+3}-\sqrt{8x+1}}{(8x+3)-(8x+1)}dx\)

= \(\int\frac{\sqrt{8x+3}-\sqrt{8x+1}}{2}dx\)

= \(\frac12[\int\sqrt{8x+3}dx-\int\sqrt{8x+1}dx]\)

= \(\frac12[\frac23\frac{(8x+3)^{3/2}}8-\frac23\frac{(8x+1)^{3/2}}8]+c\)

= \(\frac12\times\frac23\times\frac18[(8x+3)^{3/2}-(8x+1)^{3/2}]+c\)

= \(\frac1{24}[(8x+3)^{3/2}-(8x+1)^{3/2}]+c\)