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Table of Integrals

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The constant C is generally omitted except where it is the point of the entry.

• {$\displaystyle \large \int 0 dx = C$}
• {$\displaystyle \large \int k f(x)dx = k \int f(x) dx$}
• {$\displaystyle \large \int \{f(x) + g(x)\}dx = \int f(x) dx + \int g(x)dx$}
• {$\displaystyle \large \int x^n dx = {{x^{n+1}} \over {n+1}} , n \ne -1$}
• {$\displaystyle \large \int k dx = \int kx^0 dx =kx$}
• {$\displaystyle \large \int u dv = uv - \int vdu \quad\text{ "Parts" }$}
• {$\displaystyle \large \int F\{f(x)\} dx= \int F(u){{dx} \over {du}}du = \int {{F(u)} \over {f^\prime(x)}}du$}
• {$\displaystyle \large \int {{dx}\over x} = \ln |x|$}
• {$\displaystyle \large \int {1 \over {1 + x^2}}dx = \arctan x$}
• {$\displaystyle \large \int 2\sin x \cos x dx = \sin^2 x$}

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Category: Math

This is a student's notebook. I am not responsible if you copy it for homework, and it turns out to be wrong.

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March 16, 2018

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