5.4 Indefinite Integrals and the Net Change Theorem/17: Difference between revisions

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17)<math>\int{}{}1+tan^{2}x*dx = \frac{d}{dx}(tan(x))</math>


<math>\int1+tan^2 x*dx<math>
<math>\frac{d}{dx}(tan(x))=\frac{d}{dx}\left(\frac{sin(x)}{cos(x)}\right)=\frac{cos^{2}x-(-(sin(x))(sin(x))}{cos^{2}(x)}</math>
<math>\int1+\frac{sin^2x}{cos^2x}*dx<math>
 
<math>\int\frac{cos^2x+sin^2x}{cos^2x}\*dx<math>  
 
<math>\cos^2x+sin^2x=1<math>
<math>=\frac{cos^{2}x+sin^2(x))}{cos^{2}(x)}=\frac{cos^{2}x}{cos^{2}(x)}+\frac{sin^{2}x}{cos^{2}(x)}</math>
<math>\int\frac{1}{cos^2x}*dx<math>
 
<math>\int\sec^2x\*dx<math>
 
<math>tanx+C\<math>
<math>=1+tan^2(x)</math>
 
 
[[5.3 The Fundamental Theorem of Calculus/1|1]]
[[5.3 The Fundamental Theorem of Calculus/3|3]]
[[5.3 The Fundamental Theorem of Calculus/5|5]]
[[5.3 The Fundamental Theorem of Calculus/7|7]]
[[5.3 The Fundamental Theorem of Calculus/8|8]]
[[5.3 The Fundamental Theorem of Calculus/9|9]]
[[5.3 The Fundamental Theorem of Calculus/10|10]]
[[5.3 The Fundamental Theorem of Calculus/11|11]]
[[5.3 The Fundamental Theorem of Calculus/13|13]]
[[5.3 The Fundamental Theorem of Calculus/15|15]]
[[5.3 The Fundamental Theorem of Calculus/17|17]]
[[5.3 The Fundamental Theorem of Calculus/19|19]]
[[5.3 The Fundamental Theorem of Calculus/20|20]]
[[5.3 The Fundamental Theorem of Calculus/21|21]]
[[5.3 The Fundamental Theorem of Calculus/23|23]]
[[5.3 The Fundamental Theorem of Calculus/25|25]]
[[5.3 The Fundamental Theorem of Calculus/27|27]]
[[5.3 The Fundamental Theorem of Calculus/28|28]]
[[5.3 The Fundamental Theorem of Calculus/29|29]]
[[5.3 The Fundamental Theorem of Calculus/31|31]]
[[5.3 The Fundamental Theorem of Calculus/33|33]]
[[5.3 The Fundamental Theorem of Calculus/35|35]]
[[5.3 The Fundamental Theorem of Calculus/37|37]]
[[5.3 The Fundamental Theorem of Calculus/39|39]]
[[5.3 The Fundamental Theorem of Calculus/41|41]]
[[5.3 The Fundamental Theorem of Calculus/53|53]]

Revision as of 05:54, 29 August 2022

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