Exercise
$\int5x^2\sqrt{9-4x^2}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Integrate int(5x^2(9-4x^2)^(1/2))dx. The integral of a function times a constant (5) is equal to the constant times the integral of the function. First, factor the terms inside the radical by 4 for an easier handling. Taking the constant out of the radical. We can solve the integral 5\int2x^2\sqrt{\frac{9}{4}-x^2}dx by applying integration method of trigonometric substitution using the substitution.
Integrate int(5x^2(9-4x^2)^(1/2))dx
Final answer to the exercise
$\frac{45}{8}x\sqrt{9-4x^2}+\frac{405}{16}\arcsin\left(\frac{2x}{3}\right)-\frac{135}{32}x\sqrt{9-4x^2}-\frac{1215}{64}\arcsin\left(\frac{2x}{3}\right)-\frac{5}{16}\sqrt{\left(9-4x^2\right)^{3}}x+C_0$