Question

f x^4 sin (x^5+6) dx is equal to​

Answer 1

this is an answer.....

Answer 2

Given :   ∫ x⁴sin(x⁵ + 6)dx  

To Find : Evaluate Integral

Solution:

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

I = ∫ x⁴sin(x⁵ + 6)dx     ...Eq1

Let say x⁵ + 6  = y    ..Eq2

differentiating with respect to y

=> 5x⁴dx  = dy

=> x⁴dx  = dy/5    ..Eq3

From Eq2 & Eq3 substitute in Eq 1

=> I = ∫ sinydy/5

=> I = (1/5)  ∫ sinydy

=> I = (1/5) (-cosy)  + c

=> I = -(1/5)Cosy

Substitute value of y from Eq2

=>  I = -(1/5) (-cos(x⁵ + 6))  + c

∫ x⁴sin(x⁵ + 6)dx   =  -(1/5) (-cos(x⁵ + 6))  + c

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