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# Integration of cos square x

## Cos square x integration

What is Integration of cos square x dx ? In this article we will derive the integral of cosine squared x – Solving the Integral of cos2x. ∫cos2x dx = ? So Directly we can not just integrate cos2x. We have to convert cos2x into another form by using trigonometric identities to find the integration.

This integration of cos2 x dx cannot be evaluated by the directly by using any formula or integration formula, so we have to use trigonometric identity of half angle cos square x or cos2 x = (1+cos2x) / 2.

• I = ∫cos2x dx
• I =∫{(1+cos2x)/2} dx
• ⇒ I = (1/2)∫(1+cos2x) dx
• ⇒ I = (1/2) ∫1dx + (1/2) ∫cos2x dx
• Using the integral formula ∫cos kx dx = (sin kx) / k+c, we have
∫cos2x dx = (1/2) x + (1/2) (sin2x) / 2 + c
• ⇒ ∫cos2x dx = (1/2) x +(1/4) (sin2x) + c, where C is integration constant

### Integration of cos square x by using double angle formula

The double angle trigonometric identity formula: cos 2x = cos2 x – sin2 x. There is one more trigonometric identity which will be very useful to find integration of cos square x. Second trigonometric identity is sin2 x + cos2 x = 1. Now we have to combine these both trigonometric identities cos 2x = cos2 x – sin2 x and sin2 x + cos2 x = 1. After combining we will get cos 2x = 2cos2 x -1.

• cos 2x = 2cos2 x -1
• After rearranging cos2 x = ( 1+ cos 2x ) / 2, Now we can use reverse chain rule to integrate this expression.
• We will get  x/2 + ( sin 2x ) / 4 + c, where C is a integration constant.

What is the formula of Cos Square x?

cos2x = 1 – sin2x

What is the value of Cos Square θ?

cos2θ = 1 – sin2θ

Can you integrate cos 2 x?

Yes, but we have to change it in another form by using trigonometric identities cos 2x = cos2 x – sin2 x and sin2 x + cos2 x = 1. From these trigonometric identities we will get cos 2x = 2cos2 x -1.

How do you integrate Cos X?

∫ cos x dx = sin x + C

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