Integrate xcos(x) with respect to x
Using LATEX (Logarithms, Algebra, Trigonometry, Exponential and Complex numbers) to determine which variable is du and which is dv/dx. This is decided by using the above acronym. For example in this question 'x' is an algebraic variable and 'cos(x)' is a trigonometric variable, hence 'x' is du and cos(x) is dv/dx. To solve this question, we use integration by parts and use the following formula. du.dv- integral(dv.(du/dx)dx).
du = x hence du/dx = 1 (differentiate du) dv/dx = cosx hence dv = sinx (integrate dv/dx)
Plug in the values in the above equation.
Ans = xsinx + cosx + c
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Answered by Vishnu P. • Further Mathematics tutor
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