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integrate the following integral ∫ (x + 2) sqrt(3x + 5) dx

 
integrate the following integral
∫ (x + 2) sqrt(3x + 5) dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int (x+2)\sqrt{3x+5}dx
I = \frac{1}{3}\int (3x+6)\sqrt{3x+5}dx
I = \frac{1}{3}\int (3x+5)\sqrt{3x+5}dx+\frac{1}{3}\int \sqrt{3x+5}dx
I = \frac{1}{3}\int (3x+5)^{3/2}dx+\frac{1}{3}\int \sqrt{3x+5}dx
I = \frac{2(3x+5)^{5/2}}{3.5}+\frac{1}{3}\int \sqrt{3x+5}dx
I = \frac{2(3x+5)^{5/2}}{15}+\frac{2}{3}(3x+5)^{3/2}+C

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