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Worked solution

Integrate a polynomial and trigonometric sum term by term

Find the general solution of dy/dx=2x+sin⁡x+5dy/dx=2x+\sin x+5.

CJC · Lecture · Example 2

Take an antiderivative of every term

y=∫(2x+sin⁡x+5) dx=2x2/2−cos⁡x+5x+B=x2−cos⁡x+5x+By=\int(2x+\sin x+5)\,dx=2x^2/2-\cos x+5x+B=x^2-\cos x+5x+B, with arbitrary real B. Differentiating restores the supplied equation.

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Common mistakes

The constant 5 integrates to 5x, not to another arbitrary constant.

Read the hint