Answer to Question #178347 in Calculus for Phyroe

Question #178347

Integration Procedures(Itevrations by Parts)


∫ y √(y+1)dy


1
Expert's answer
2021-04-20T16:36:38-0400
"\\int y\\sqrt{(y+1)}dy=\\int (y+1-1)\\sqrt{(y+1)}dy"

"=\\int (y+1)^{3\/2}dy-\\int \\sqrt{(y+1)}dy"


"=\\dfrac{2}{5} (y+1)^{5\/2}-\\dfrac{2}{3} (y+1)^{3\/2}+C"

"=\\dfrac{2}{15} (y+1)^{3\/2}(3y+3-5)+C"

"=\\dfrac{2}{15} (y+1)^{3\/2}(3y-2)+C"



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