INTEGRAL CALCULUS dy Please use of the following as guide in solving the assignment. Antidifferentiation Differential Equation Chain Rule Logarithmic Funtion Exponential Function Integration by Parts...

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INTEGRAL CALCULUS

  1. dy































Please use of the following as guide in solving the assignment.

  1. Antidifferentiation

  2. Differential Equation

  3. Chain Rule

  4. Logarithmic Funtion

  5. Exponential Function

  6. Integration by Parts

  7. Integrals Yielding Inverse Trigonometric Funtion

  8. Integrals Involving Hyperbolic Functions

  9. Inverse Hyperbolic Function

  10. Integration of Algebraic Functions by Trigonometric Substitution

  11. Trigonometric Integrals

  12. Integration of Rational Functions

  13. Integration by other Substitution Techniques




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INTEGRAL CALCULUS Created with an evaluation copy of Aspose.Words. To discover the full versions of our APIs please visit: https://products.aspose.com/words/ y3(1-2y4)5 dy sec25xdx 13-2xdx sin3tcos3t-1dt 1+e2xexdx cos33x3sin3xdx tan5xsec3xdx x2x2+6dx dww2w2-7 2x-1x2-1dx dtt+22(t+1) 82cos2x+1dx sin5?d? x2e4xdx 24sinh5ydy Created with an evaluation copy of Aspose.Words. To discover the full versions of our APIs please visit: https://products.aspose.com/words/ Please use of the following as guide in solving the assignment. Antidifferentiation Differential Equation Chain Rule Logarithmic Funtion Exponential Function Integration by Parts Integrals Yielding Inverse Trigonometric Funtion Integrals Involving Hyperbolic Functions Inverse Hyperbolic Function Integration of Algebraic Functions by Trigonometric Substitution Trigonometric Integrals Integration of Rational Functions Integration by other Substitution Techniques






INTEGRAL CALCULUS 1. dy 2. 3. 4. 5. 6. 7. 8. 9. 10. 1. 2. 3. 4. 5. 6. Please use of the following as guide in solving the assignment. 1. Antidifferentiation 2. Differential Equation 3. Chain Rule 4. Logarithmic Funtion 5. Exponential Function 6. Integration by Parts 7. Integrals Yielding Inverse Trigonometric Funtion 8. Integrals Involving Hyperbolic Functions 9. Inverse Hyperbolic Function 10. Integration of Algebraic Functions by Trigonometric Substitution 11. Trigonometric Integrals 12. Integration of Rational Functions 13. Integration by other Substitution Techniques
Answered Same DayDec 23, 2021

Answer To: INTEGRAL CALCULUS dy Please use of the following as guide in solving the assignment....

Robert answered on Dec 23 2021
119 Votes
Sol: (1)
 
3
5
41 2
y
dy
y

Substitute
4
3
1 2
8
u y
du y dy
 
 

Now,
   
 
 
 
   
3
5 5
4
3
5
5
4
3 5 1
5
4
3 4
5
4
3
5 4
4 4
1 1
81 2
1
81 2
1

8 5 11 2
1
8 41 2
1
1 2 32 1 2
y
dy du
uy
y
dy u du
y
y u
dy C
y
y u
dy C
y
y
dy C
y y

 

 

 

 
   
  
 
   
 
 
 
 
 



Sol: (2)  2sec 5x dx
 2 int sec 5 , 5 5 :For the egrand x substitute u x and du dx 
   
 
 
2 21sec 5 sec
5
1
tan
5
1
tan 5
5
x dx u du
u C
x C

 
 
 

Sol: (3)
1
3 2
dx
x


1
int , 3 - 2 -2 :
3 2
For the egrand substitute u x and du dx
x
 


 
 
1 1 1
3 2 2
1
log
2
1
log 3 2
2
dx du
x u
u C
x C
 

  
   
 
Sol: (4)
sin 3
cos3 1
t
dt
t 

sin 3
int , cos3 1 3sin 3 :
cos3 1
t
For the egrand substitute u t and du tdt
t
   


 
 
sin 3 1 1
cos3 1 3
1
log
3
1
log cos3 1
3
t
dt dt
t u
u C
t C
 

  
   
 

Or

sin 3 2 3
log sin
cos3 1 3 2
t t
dt C
t
  
    
   

Sol: (5)
21 x
x
e
dx
e


2 2
2
1 1
1
1
x x
x x x
x x
x x
x
x
x
x
e e
dx dx dx
e e e
e dx e dx
e e C
e C
e
e
C
e



 
 
   
   

 
  
 
Sol: (6)
 
 
3
3
cos 3
sin 3
x
dx
x

 
 
      
 
3
3
2
3 3
2
cos 3
int ,
sin 3
sin 3 sin 3 cos 3
cos 3

x
For the egrand
x
substitute u x and du x x dx
x
du dx
u

 


 
 
    
 
 
 
 
     
23
3 3
6
2
6
7
2 8
2 8
3 3
cos 3 1 sin 3cos 3
sin 3 sin 3
1
1
2 8
sin 3 sin 3
2 8
x xx
dx dx
x x
u
u du
u
u udu
u u du
u u
C
x x
C




 
 
   
     
   
   
   
     
   
   
 



Sol: (7)
5 3tan secx xdx
5 3 2 2 For the integrand tan sec , use the triginometric identity tan sec 1:x x x x 
      
2
5 3 3...
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