Evaluate the Integral. Show All Steps

Question

Evaluate the Integral. Show All Steps. If possible attach a video going through the problem.

Answer 1

x = 5/2tanu; dx = 5/2sec²udu; ∫x²/(4x² + 25)^3/2dx = ∫25/4tan²u/(5³sec³u)·5/2sec²udu = 1/8∫tan²u/secudu =

1/8∫(secu - cosu)du = 1/8[ln(secu + tanu) - sinu] + C = 1/8[ln(2/5x + √(1 + 4/25x²)) - 2/5x/√(1 + 4/25x²)] + C