Determine the following indefinite integral. \int (4\sqrt{x}-\frac{4}{\sqrt{x}})dx

Baublysiz 2021-11-21 Answered
Determine the following indefinite integral.
(4x4x)dx
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Expert Answer

Befoodly
Answered 2021-11-22 Author has 17 answers
Step 1: Given that
Determine the following indefinite integral.
(4x4x)dx
Step 2: Solve
(4x4x)dx=4x41xdx
=4[x12+112+1]4[x12+112+1]
=83[x32]8x
Step 3: Check by differentiation
y=83x328x12
dydx=83×32×x3218×12×x121
dydx=4x124x12
dydx=4x4x
Hence Verified.
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inenge3y
Answered 2021-11-23 Author has 20 answers
Step 1: Expand.
4x4xdx
Step 2: Use Sum Rule: f(x)+g(x)dx=f(x)dx+g(x)dx.
4xdx4xdx
Step 3: Use Power Rule: xndx=xn+1n+1+C.
8x3234xdx
Step 4: Use Constant Factor Rule: cf(x)dx=cf(x)dx.
8x32341xdx
Step 5: Since 1x=x12, using the Power Rule, x12dx=2x12
8x3238x+C
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