Evaluate the indefinite integral. (Use C for the constant of integration.)

Question

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a+bx⁹ / 10ax+bx^10. dx

Answer 1

Let u = 10ax + bx¹⁰

Then du = 10(a + bx⁹)dx. So, (a + bx⁹)dx = (1/10)du

Therefore, ∫[(a + bx⁹) / √(10ax + bx¹⁰)]dx = (1/10)∫ (du / √u) = (1/5)√u + C = (1/5)√{10ax + bx¹⁰) + C