Evaluate the indefinite integral. \int \frac{a+bx^{2}}{\sqrt{3

skomminbv

skomminbv

Answered question

2021-12-06

Evaluate the indefinite integral.
a+bx23ax+bx3dx

Answer & Explanation

barcelodurazo0q

barcelodurazo0q

Beginner2021-12-07Added 13 answers

Step 1
Given integral:
a+bx23ax+bx3dx
Step 2
Now,
Apply u-substitution:
u=3ax+bx3
Differentiate both sides:
du=3adx+3bx2dx
du3=(a+bx2)dx
Therefore,
a+bx23ax+bx3dx=du3u
=13u12du
Apply the Power Rule: xadx=xa+1a+1,a1
=13u12+112+1
=23u
Substitute back u=3ax+bx3:
=233ax+bx3
Add a constant to the solution:
=233ax+bx3+C

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