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الـ(Integration) هو عملية عكسية للـ (differentiation)

اذا كان f,g   (differentiable functions)  فان

\(\frac{d}{d x}[f(x) g(x)]=f(x) g^{\prime}(x)+g(x) f^{\prime}(x)\)

in the notation for indefinite integrals this equation becomes

\( \int f(x) g^{\prime}(x) d x=f(x) g(x)-\int g(x) f^{\prime}(x) dx \)

وهذه الصيغة تُسمى بـ (the formula for integration by parts)

يوجد ايضا طريقة اخرى فى الـ (integration by parts)

نفرض ان  u = f(x) و v = g(x) ثم عمل differentiation  لـ u,v  هنحصل على

 du = f'(x)  و dv = g'(x)

اذن :

\(\int u d v=u v-\int v d u\)

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