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evaluate ∫ (sqrt(x)( ax^2 + bx + c)) dx

evaluate
∫ (sqrt(x)( ax^2 + bx + c)) dx

Grade:12

2 Answers

Sunil Raikwar
askIITians Faculty 45 Points
6 years ago

∫ (sqrt(x)( ax^2 + bx + c)dx

=​∫ (x^1/2(ax^2 +bx +c)dx

=​∫ (ax^5/2 +bx^3/2 +cx^1/2)dx

=2​ax^7/2 /7 +2bx^5/2 /5 +2cx^3/2 /3 +K {we know that​∫x^ndx =(x^(n+1) /(n+1)}
Here K is a constant
Karthick vel
20 Points
6 years ago
make ax2+bx+c in to form of a((x-b/2)2+(c-b2/4)). then put (x-b/2)=(c-b2/4)^.5*tany.
then integrate it. simple

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