Final Answer
Step-by-step Solution
Specify the solving method
Use the odd-even identity $\sin(-\theta)=-\sin(\theta)$
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$\int-x^3\sin\left(6x\right)dx$
Learn how to solve integral calculus problems step by step online. Find the integral int(x^3sin(-6x))dx. Use the odd-even identity \sin(-\theta)=-\sin(\theta). The integral of a function times a constant (-1) is equal to the constant times the integral of the function. We can solve the integral \int x^3\sin\left(6x\right)dx by applying the method of tabular integration by parts, which allows us to perform successive integrations by parts on integrals of the form \int P(x)T(x) dx. P(x) is typically a polynomial function and T(x) is a transcendent function such as \sin(x), \cos(x) and e^x. The first step is to choose functions P(x) and T(x). Derive P(x) until it becomes 0.