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The integral of a function times a constant ($n$) is equal to the constant times the integral of the function
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$n\int\left(2x\right)^2dx$
Learn how to solve integral calculus problems step by step online. Find the integral int(n(2x)^2)dx. The integral of a function times a constant (n) is equal to the constant times the integral of the function. Rewrite the expression \left(2x\right)^2 inside the integral in factored form. The integral of a function times a constant (4) is equal to the constant times the integral of the function. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, such as 2.