Evaluate the integral. \int (x^{6}-7x)^{4}dx

osteoblogda

osteoblogda

Answered question

2021-12-30

Evaluate the integral.
(x67x)4dx

Answer & Explanation

Thomas Lynn

Thomas Lynn

Beginner2021-12-31Added 28 answers

Step 1 
Consider the integral
(x67x)4 dx  
Step 2 
let I=(x67x)4 dx  
remove x from the bracket
I=x4(x57)4 dx  
put u=x57 
differentiating it wrt x we have 
du=5x4 dx  
du5=x4 dx  
Replace it with the integral
I=u4du5 
I=15u4du 
I=15(u55)+c 
I=(x57)525+c

Foreckije

Foreckije

Beginner2022-01-01Added 32 answers

(x67x)4dx
x2428x19+294x141372x9+2401x4dx
x24dx28x19dx+294x14dx1372x9dx+2401x4dx
x25257x205+98x155686x105+2401x55
x2525+7x20+98x15686x10+2401x55
x2525+7x20+98x15686x10+2401x55+C
karton

karton

Expert2022-01-04Added 613 answers

(x67x)4dx=15(u7)4du(u7)4du=v4dv=v55=(u7)5515(u7)4du=(u7)525=(x57)525(x67x)4dx=(x57)525+C

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