Question

integration x^4sin (x^5+6)dx is equal.to​
A) cos(x^5+6)+c
B) -cos(x^5+6)+c
C) cos(x^5+6)+c/5
D) -cos(x^5+6)+c/5
​

Answer 1

Given :   x⁴sin(x⁵ + 6)dx

To find : Integration

Solution:

Let say I is the integral of  x⁴sin(x⁵ + 6)dx

=> I = ∫x⁴sin(x⁵ + 6)dx

Assume that

x⁵ + 6  = y

differentiating wrt y

=> 5x⁴ .dx/dy + 0  =  1

=> x⁴ .dx = dy/5

I = ∫ sin(y)dy /5

=> I = (1/5)  ∫ sin(y)dy

=> I = (1/5)  (- Cosy + c)

=> I = (1/5)  (- Cos(x⁵ + 6) + c)

=> I =  (- Cos(x⁵ + 6) + c) /5

=>  ∫x⁴sin(x⁵ + 6)dx  = (- Cos(x⁵ + 6) + c) /5

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