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Learn how to solve tabular integration problems step by step online. Find the integral int((x^2-2x+3)(cos(3x)+sin(3x)))dx. Rewrite the integrand \left(x^2-2x+3\right)\left(\cos\left(3x\right)+\sin\left(3x\right)\right) in expanded form. Expand the integral \int\left(x^2\cos\left(3x\right)+x^2\sin\left(3x\right)-2x\cos\left(3x\right)-2x\sin\left(3x\right)+3\cos\left(3x\right)+3\sin\left(3x\right)\right)dx into 6 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int x^2\cos\left(3x\right)dx results in: \frac{1}{3}x^2\sin\left(3x\right)+\frac{2}{9}x\cos\left(3x\right)-\frac{2}{27}\sin\left(3x\right). The integral \int x^2\sin\left(3x\right)dx results in: -\frac{1}{3}x^2\cos\left(3x\right)+\frac{2}{9}x\sin\left(3x\right)+\frac{2}{27}\cos\left(3x\right).
Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more
Tabular integration is a special technique to solve certain integrals by parts usually made up of two functions: one polynomial and the other transcendent, like the exponential function or the sine. The method consists of deriving the polynomial function several times (until it becomes zero), and integrating the transcendent function several times. This method is usually applied when both functions can be easily derived and integrated multiple times.
