Final Answer
$\frac{1}{2}x^{4}-4x^2+C_0$
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Step-by-step Solution
Problem to solve:
$\int2x\left(x^2-4\right)dx$
Specify the solving method
1
The integral of a function times a constant ($2$) is equal to the constant times the integral of the function
$2\int x\left(x^2-4\right)dx$
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$2\int x\left(x^2-4\right)dx$
Learn how to solve problems step by step online. Find the integral int(2(x^2-4)x)dx. The integral of a function times a constant (2) is equal to the constant times the integral of the function. Rewrite the integrand x\left(x^2-4\right) in expanded form. Expand the integral \int\left(x^{3}-4x\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral 2\int x^{3}dx results in: \frac{1}{2}x^{4}.
Final Answer
$\frac{1}{2}x^{4}-4x^2+C_0$