104k views
13 votes
Find the indefinite integral

Find the indefinite integral-example-1

1 Answer

10 votes

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\\\\\\

========================================================

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\\\\\\

User Cydrick Trudel
by
8.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories