Final Answer
$-\frac{1}{2}\sqrt{\left(1-2x^2\right)^{3}}+C_0$
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Step-by-step Solution
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1
The integral of a function times a constant ($3$) is equal to the constant times the integral of the function
$3\int x\sqrt{1-2x^2}dx$
Learn how to solve integrals with radicals problems step by step online.
$3\int x\sqrt{1-2x^2}dx$
Learn how to solve integrals with radicals problems step by step online. Integrate int(3x(1-2x^2)^1/2)dx. The integral of a function times a constant (3) is equal to the constant times the integral of the function. First, factor the terms inside the radical by 2 for an easier handling. Taking the constant out of the radical. We can solve the integral 3\int\sqrt{2}x\sqrt{\frac{1}{2}-x^2}dx by applying integration method of trigonometric substitution using the substitution.
Final Answer
$-\frac{1}{2}\sqrt{\left(1-2x^2\right)^{3}}+C_0$