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The derivative of the second term is 1 2 (1 x 2) 1= ( x2x) = 1p 1 x2:Hence the derivative of the function y= sin x2 + p 1 x2 is y0= 2x p 1 x4 x p 1 x2: Integrals producing inverse trigonometric functions. The above formulas for the the derivatives imply the following formulas for the integrals. Z 1 p 1 x2 dx= sin 1 x+ c Z 1 x2 + 1 dx= tan 1x+ c ...

For antiderivatives involving both exponential and trigonometric functions, see List of integrals of exponential functions. For a complete list of antiderivative functions, see lists of integrals.

Common Derivatives and Integrals Visit http://tutorial.math.lamar.edu for a complete set of Calculus I & II notes. © 2005 Paul Dawkins Inverse Trig Functions 1

Antiderivatives of Basic Trigonometric Functions ; cos · | ; cot(x)dx · sin · | ; sec(x)dx · sec · + ; csc(x)dx · csc · + ...

Common Derivatives and Integrals ... Trig Substitutions If the integral contains the following root use the given substitution and formula. 222sinandcos221sin a

CALCULUS TRIGONOMETRIC DERIVATIVES AND INTEGRALS. TRIGONOMETRIC DERIVATIVES d dx(sin(x)) = cos(x) · x0 ... INVERSE TRIG INTEGRALS. / sinn(x) = - 1.

Trig Cheat Sheet tano - sino cotors te cose sin. Definition of the Trig Functions. Right triangle definition ... Common Derivatives and Integrals.

When finding the derivatives of trigonometric functions, non-trigonometric derivative rules are often incorporated, as well as trigonometric derivative rules. Looking at this function, one can see that the function is a quotient. Therefore, use derivative rule 4 on page 1, the Quotient Rule, to start this problem ...

CALCULUS TRIGONOMETRIC DERIVATIVES AND INTEGRALS STRATEGY FOR EVALUATING R sinm(x)cosn(x)dx (a) If the power n of cosine is odd (n =2k +1), save one cosine factor and use cos2(x)=1sin2(x)to express the rest of the factors in terms of sine:

The following is a list of integrals (antiderivative functions) of trigonometric functions. For antiderivatives involving both exponential and trigonometric ...

When finding the derivatives of trigonometric functions, non-trigonometric derivative rules are often incorporated, as well as trigonometric derivative ...

Common Derivatives and Integrals ... Trig Substitutions If the integral contains the following root use the given substitution and formula. 222sinandcos221sin a abxx b-Þ=qqq=-222secandtan22sec1 a bxax b-Þ=qqq=-222tanandsec221tan a abxx b +Þ=qqq=+ Partial Fractions If integrating () Px dx Qx

integral, (())() () bgb( ) aga òòfgxg¢ xdx= fudu . Integration by Parts The standard formulas for integration by parts are, bbb aaa òudv=uv-vduòòudv=-uvvdu Choose u and dv and then compute du by differentiating u and compute v by using the fact that v= …

Recall the definitions of the trigonometric functions. ... It is assumed that you are familiar with the following rules of differentiation.

Trig Substitutions. If the integral contains the following root use the given substitution and formula. 2. 2 2. 2. 2 sin and cos. 1 sin.

List of Derivatives of Trig & Inverse Trig Functions; List of Derivatives of Hyperbolic & Inverse Hyperbolic Functions; List of Integrals Containing cos; List of Integrals Containing sin; List of Integrals Containing cot; List of Integrals Containing tan; List of Integrals Containing sec; List of Integrals Containing csc

List of Derivatives of Trig & Inverse Trig Functions; List of Derivatives of Hyperbolic & Inverse Hyperbolic Functions; List of Integrals Containing cos; List of Integrals Containing sin; List of Integrals Containing cot; List of Integrals Containing tan; List of Integrals Containing sec; List of Integrals Containing csc

g(x)dx = f(x) + C. That is, every time we have a differentiation formula, we get an integration formula for nothing. Here is a list of some of ...

CALCULUS TRIGONOMETRIC DERIVATIVES AND INTEGRALS STRATEGY FOR EVALUATING R sinm(x)cosn(x)dx (a) If the power n of cosine is odd (n =2k +1), save one cosine factor and use cos2(x)=1sin2(x)to

This section covers: Derivatives of the Inverse Trig Functions Integrals ... To do this, just take the greatest common factor (GCF) of the constant out, ...

List of Derivatives of Simple Functions; List of Derivatives of Log and Exponential Functions; List of Derivatives of Trig & Inverse Trig Functions; List of Derivatives of Hyperbolic & Inverse Hyperbolic Functions; List of Integrals Containing cos; List of Integrals Containing sin; List of Integrals Containing cot; List of Integrals Containing tan