Question

Find the indefinite integral

Answer 1

Answer:
`\displaystyle (2)/(3)x^(3/2) + (2)/(5)x^(1/2)+C\\\\\\`

This is equivalent to
`(2)/(3)√(x^3) + (2)/(5)√(x)+C\\\\\\`

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Work Shown:

`\displaystyle \int\left(√(x) + (1)/(5√(x))\right)dx\\\\\\ \displaystyle \int\left(√(x)\right)dx + \int\left((1)/(5√(x))\right)dx\\\\\\ \displaystyle \int\left(x^(1/2)\right)dx + \int\left((1)/(5)x^(-1/2)\right)dx\\\\\\ \displaystyle \int\left(x^(1/2)\right)dx + (1)/(5)\int\left(x^(-1/2)\right)dx\\\\\\`

`\displaystyle (1)/(1+1/2)x^(1+1/2) + (1)/(5)*(1)/(1+(-1/2))x^(1+(-1/2))+C\\\\\\ \displaystyle (1)/(3/2)x^(3/2) + (1)/(5)*(1)/(1/2)x^(1/2)+C\\\\\\ \displaystyle (2)/(3)x^(3/2) + (1)/(5)*2x^(1/2)+C\\\\\\ \displaystyle (2)/(3)x^(3/2) + (2)/(5)x^(1/2)+C\\\\\\`