Question

integration of 8x+17/under root (4x+7)dx

Answer 1

$I= \int\limits^a_b {\frac{8x+17}{\sqrt{4x+7}}} \, dx \\\\Let\ 4x+7=t^2,\ \ dx=t\ dt/2\\\\8x+17=2t^2+3\\\\I= \int\limits^a_b {\frac{2t^2+3}{t}} \, tdt/2\\\\= \int\limits^a_b {t^2+3/2} \, dx \\\\= t^3/3+3/2t+C\\\\=\frac{1}{6}\sqrt{4x+7}\ [8x+23]+C$

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