Evaluate the following integrals: ∫ (6x+5)√(6+x-2x^2)dx

Question

Evaluate the following integrals:  \(\int(6x+5)\sqrt{6+x-2x^2}dx\)

∫ (6x+5)√(6+x-2x²)dx

Answer 1

To Find : \(\int(6x+5)\sqrt{6+x-2x^2}dx\)

Now, let 6x + 5 be written as\(\cfrac{13}{2}-\cfrac{3}{2}\)(1 - 4x)and split

Therefore ,

Therefore,