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**Integrals**

- Integrals – a definition
- The fundamental theorem of calculus
- The connection between the definite and indefinite integral
- Some standard integrals

**Integration by substitution **

**Integration by parts**

- Integration by parts
- One function is in the form
*x*and the other can be integrated at least^{n}*n*times - One of the functions is sin(
*bx*) or cos(*bx*) or a linear combination of them, the other is an exponential function - We have only one function, but one we can differentiate, e.g. arcsine,
- One is a logarithm

**Some various integrals**

- The integral of sin(
*x*)cos(*x*)*dx,* - The integral of 1/sqrt(1-
*x*^2)*dx*, - The integral of one over sqrt(
*x*^2+1)*dx,* - The integral of sqrt(1-
*x*^2)*dx*, - The integral of sqrt(
*x*^2-1)*dx*, - The integral of sqrt(
*x*^2+1)*dx*,

**A rather peculiar rule
**

**Some special integrals**

- The integral
- The integral
- The integral
- The integral
- The integral , a second way.

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