# 9.588+ Table Of Basic Integrals And Derivatives

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Integration by parts the standard formulas for integration by parts are bb b aa a udv uv vdu udv uv vdu choose uand then compute and dv du by differentiating u and compute v by using the fact that v dv. Tables of basic derivatives and integrals ii derivatives d dx xa axa1 d dx ex ex d dx sinx cosx d dx cosx sinx d dx tanx sec2 x d dx cotx csc2 x d dx secx secxtanx d dx cscx cscxcotx d dx lnx 1 x d dx ax ax lna d dx arcsinx 1 1x2 d dx arccosx 1 1x2 d dx arctanx 1 1x2 d dx arccotx 1 1x2 d dx arcsecx 1 x x2 1 d dx arccscx 1 x x2 1.

### Basic differentiation rules basic integration formulas derivatives and integrals c houghton mifflin company inc.

**Table of basic integrals and derivatives**. This page lists some of the most common antiderivatives. The clustrmap is periodically and automatically archived and its counters reset so the total is smaller. Table of basic integrals1 1 z xn dx 1 n1 xn1.

Power rule x 1 dx d 8. Common derivatives and integrals derivative rules. Table of basic derivatives let u ux be a differentiable function of the independent variable x that is ux exists.

Derivative involving absolute value uu 0. Not to mention their servers gave up the ghost turned into zombies on 25 march 2015 brains. Of course you use trigonometry commonly called trig in pre calculus.

As you can see integration reverses differentiation returning the function to its original state up to a constant c. Product rule uv uv vu dx d 4. U d dx x3 4x 134 3 4 x3 4x 1143x2 4 d dx u 1 2 uu d dx 2 4x2 7x5 1 2 2 4x2 7x5 8x 35x4 d dx c 0 c is a constant d dx.

Sum and difference rule u v u v dx d 3. D dx un nu n1. Free integral calculator solve indefinite definite and multiple integrals with all the steps.

Constant multiple rule cu cu dx d where c is a constant. Integral b gb a ga f g x g x dx f u du. A the power rule.

Quotient rule v2 vu uv v u dx d 5. N 6 1 2 z 1 x dx lnjxj 3 z u dv uv z vdu 4 z e xdx e 5 z ax dx 1 lna ax 6 z lnxdx xlnx x 7 z sinxdx cosx 8 z cosxdx sinx 9 z tanxdx lnjsecxj 10 z secxdx lnjsecxtanxj 11 z sec2 xdx tanx 12 z secxtanxdx secx 13 z a a2 x2 dx tan 1 x a 14 z a a2 x2 dx 1 2 ln xa x a 15 z 1 p a2 2x dx sin 1 x a 16 z a x p x 2 a. The table below shows you how to differentiate and integrate 18 of the most common functions.

While differentiation has easy rules by which the derivative of a complicated function can be found by differentiating its simpler component functions integration does not so tables of known integrals are often useful. Power rule u nu u dx d n 1 7. Constant rule c 0 dx d 6.

Type in any integral to get the solution steps and graph this website uses cookies to ensure you get the best experience. Integration is the basic operation in integral calculus.