Evaluate : ∫ (7x + 3)/√(3 + 2x - x^2)

Question

Evaluate :

\(\int \frac{7x + 3}{\sqrt{3 + 2x - x^2}}dx\)

∫ (7x + 3)/√(3 + 2x - x²)

Answer 1

∫ (7x + 3)/√(3 + 2x - x²)

Let 7x + 3 = A[d/dx(3 + 2x – x²)] + B

7x + 3 = A(2 – 2x) + B 

∴ 7x + 3 = -2Ax + (2A + B)

Comparing the coefficient of x and constant on both the sides, we get

-2A = 7 and 2A + B = 3

In I₁, put 3 + 2x - x² = t

∴ (2 - 2x)dx = dt