Question

Find the value of

$\displaystyle\int 2x\:cos(x^2-5)$

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Answer 1

Answer:

∫2x cos(x²-5) = sin(x²-5) +C

Step-by-step explanation:

Given,

∫ 2x cos(x² - 5) dx

Let x² - 5 = z

dz / dx = 2x , or, dx = 1/2x dz

Then, our integral becomes,

∫ 2x cos(z) dz / 2x

= ∫ cos(z) dz

Using formula, ∫ cosx = sinx + C

= sin(z) + C

Put the value of z again:

= sin(x²-5) +C