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Problem with an integral?
Hi.
How do I integrate the following function:
∫ (x+1)*sqrt(5-x) dx.
I want to know how to do it using substitution, not integration by parts. Please show how you do it and explain the steps.
Thank you!
2 Answers
- ?Lv 61 decade agoFavorite Answer
Let u = 5-x ; x = 5-u
du = -dx
∫ (x+1)*√(5-x) dx = ∫ (6-u)*√u *(-du)
= ∫ (u-6)√u du.
= ∫ u√u du - ∫ 6√u du
= ∫ u^(3/2) du - 6∫ u^(1/2) du
= u^(5/2) /(5/2) - 6u^(3/2) /(3/2) + c
= (2/5)u^(5/2) - 4u^(3/2) + c
= (2/5)(5-x)^(5/2) - 4(5-x)^(3/2) + c
