Integrales

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Common Integrals
1.

2.

3.

4.

5.

6.

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27.28.

29.

sech 30.

or

csch 31.

or

sech 32. csch 2 u du =-coth u 33.

34. coth 2 u du = u -coth u 35.

36.

37.

sech 38.

sech u

csch ucoth u du = -csch u 39.

40.coth 41.

42.

43.

or 44.

45.

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48.

COMMO SUBSTITUTIO S
1.

where 2.

where 3.

where 4.

where 5.

where

6.

where 7.

where 8.

where 9.

whereThe Derivative
Definition of The Derivative

The derivative of the function f(x) at the point

is given and denoted by

Some Basic Derivatives
In the table below, u,v, and w are functions ofthe variable x. a, b, c, and n are constants (with some restrictions whenever they apply). function and e the natural base for designate the natural logarithmic .

. Recall that

Chain Rule Thelast formula

is known as the Chain Rule formula. It may be rewritten as

Another similar formula is given by

Derivative of the Inverse Function

The inverse of the function y(x) is thefunction x(y), we have

Derivative of Trigonometric Functions and their Inverses

Recall the definitions of the trigonometric functions

Derivative of the Exponential and Logarithmic functionsRecall the definition of the logarithm function with base a > 0 (with

):

Derivative of the Hyperbolic functions and their Inverses

Recall the definitions of the trigonometric functions Higher Order Derivatives
Let y = f(x). We have:

In some books, the following notation for higher derivatives is also used:

Higher Derivative Formula for the Product: Leibniz Formula

whereare the binomial coefficients. For example, we have

Table of Trigonometric Identities
Reciprocal identities

Pythagorean Identities

Quotient Identities

Co-Function Identities

Even-Odd...
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