Find indefinite integral. \int (x^{1/2}+3x^{-2/3})dx

akutagawatj

akutagawatj

Answered question

2021-12-07

Find indefinite integral.
(x12+3x23)dx

Answer & Explanation

Charles Clute

Charles Clute

Beginner2021-12-08Added 17 answers

Step 1
Let the given integral be y −
y=(x12+3x23)dx
Identity to be used −
xndx=x(n+1)n+1+C
Step 2
Using identity in the given function −
y=[x(12+1)(12+1)]+3[x(23+1)(23+1)]+C
y=[x3232]+3[x1313]+C
y=23x32+3(3)x13+C
y=23x32+9x13+C
Hence, the integration of given integral is −
(x12+3x23)dx=23x32+9x13+C

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