Question

Indefinite Integrals\[\int\limits_{}^{}(5s+3)^{2}ds\]

Answer 1

You could start off using u-substitution with u = 5s+3 and du = 5 ds so the integral can be simplified to \[\frac{ 1 }{ 5 } \int\limits u^2 du\]

Answer 2

I don't get that

Answer 3

Do you understand the concept of u-substitution? You are basically simplifying the integral in order to solve it so by saying the u is equal to 5s+3 you can figure out what du, or the derivative, of u is. In this case du would be equal to 5 ds so you would have the integral\[\int\limits 5u^2 du\] this is equivalent to\[\int\limits 5(5s+3)^2 ds\] so in order to simplify it to the original integral you multiply the integral by the inverse, in this case 1/5 and you end up with \[\frac{ 1 }{ 5 } \int\limits u^2 du\]

Answer 4

and where do you go from there? the book gives an answer of \[\frac{ (5s+3)^{3} }{ 15+C }\]

Answer 5

Then you could find the integral which would be \[\frac{ 1 }{ 5 } * \frac{ u^3 }{ 3 } + c\] and you substitute the definition of u into the integral so that the integral is equal to \[1/5 * \frac{ (5s+3)^3 }{ 3 } + c\] and you could simplify that to the answer that you have

Answer 6

OH, so you do. That makes sense lol. Thanks I appreciate your time

Answer 7

No problem :) glad you understood it