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integrate the following integral ∫ (5x – 3)sqrt(2x – 1) dx

 
integrate the following integral
∫ (5x – 3)sqrt(2x – 1) dx

Grade:12

1 Answers

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

I = \int (5x-3)\sqrt{2x-1}dx
I = \int (5x-\frac{5}{2}-\frac{1}{2})\sqrt{2x-1}dx
I = \int (5x-\frac{5}{2})\sqrt{2x-1}dx-\frac{1}{2}\int \sqrt{2x-1}dx
I = \frac{5}{2}\int (2x-1)\sqrt{2x-1}dx-\frac{1}{2}\int \sqrt{2x-1}dx
I = \frac{5}{2}\int (2x-1)^{3/2}dx-\frac{1}{2}\int \sqrt{2x-1}dx
I = \frac{5}{2}\frac{(2x-1)^{5/2}}{\frac{5}{2}.2}-\frac{1}{2}\int \sqrt{2x-1}dx
I = \frac{(2x-1)^{5/2}}{2}-\frac{1}{2}\frac{(2x-1)^{3/2}}{\frac{3}{2}.2}
I = \frac{(2x-1)^{5/2}}{2}-\frac{(2x-1)^{3/2}}{6}+c

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