Question

Find the value of ∫2x cos (x2 – 5).

Answer 1

$\huge \fbox{ \underline \purple{Answer }}$

Solution:

Let, I = ∫2xcos(x² – 5).dx

Let x² – 5 = t …..(1)

2x.dx = dt

Substituting these values, we have

I = ∫cos(t).dt

= sin t + c …..(2)

Substituting the value of 1 in 2, we have

= sin (x² – 5) + C

Hence the value of ∫2x cos (x² – 5) = sin (x² – 5) + C

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Answer 2

Given :  2x cos (x² – 5)

To Find : Integrate with respect to x .

Solution:

∫2x cos (x² – 5)  dx

substitute x² – 5 = y

=> 2xdx = dy

= ∫  cosy dy

= siny  +  C

= sin(x² – 5)  + C

∫2x cos (x² – 5)  dx = sin(x² – 5)  + C

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