Question

anyone please just tell me the answers ?

Answer 1

Answer:

Tell the book name

Step-by-step explanation:

Plz

Answer 2

∫ ( 12x³/(3x⁴ + 1) )dx  = log(3x⁴ + 1)  + c  

Step-by-step explanation:

Taking one problem

∫ ( 12x³/(3x⁴ + 1) )dx

Let say  y = 3x⁴ + 1

=> dy/dx  = 4x³

=> dy = 4x³ dx

=> 3 * dy = 3 * 4x³ dx

=> 3 . dy  = 12x³ dx

putting 12x³ dx  = 3dy

& 3x⁴ + 1 = y

we get

∫    3dy/y

= 3 ∫  dy/y

= log(y)  + c  

putting y = 3x⁴ + 1

=  log(3x⁴ + 1)  + c  

Hence ∫ ( 12x³/(3x⁴ + 1) )dx =  log(3x⁴ + 1)  + c  

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