Integral of Cot2x

The integral of cot2x is equal to (1/2) ln |sin2x| + C, where C is the integration constant. We can calculate the integration cot2x using the u-substitution method. Mathematically, we can write the integral of cot2x as ∫cot2x dx = (1/2) ln |sin2x| + C. Also, we know that cot2x can be expressed as the ratio of cos2x and sin2x. Therefore, after expressing cot in terms of sin and cos, we can determine the integral of cot2x using the quotient rule of integration.

In this article, we will explore the integral of cot2x, determine its formula using different methods of integration. We will also evaluate the integral of cot square x using integration formulas. In this article, we will solve different examples related to the concept for a better understanding.

The integral of cot2x is equal to (1/2) ln |sin2x| + C, where C is the integration constant. This formula of integration of cot2x can be determined using different integration formulas including the u-substitution method and expressing cot2x as the ratio of cos2x and sin2x. In the next section, let us go through the formula for the integral of cot2x.

The formula for the integral of cot2x is ∫cot2x dx = (1/2) ln |sin2x| + C, where C is the constant of integration. This formula for the integration of cot2x can be used to determine its definite integral with different limits. The image given below shows the formula for the integral of cot2x:

Now, we will prove that the integral of cot2x is equal to (1/2) ln |sin2x| + C using the u-substitution method of integration. For a function f(x) = cot2x, assume 2x = u. Differentiating both sides we have, 2 dx = du which implies dx = du/2. Also, we know that the integral of cotx is equal to ln |sin x| + K, where K is the integration constant. Using this formula, we have

∫cot2x dx = (1/2) ∫cot u du

= (1/2) ( ln |sin u| + K)

= (1/2) ln |sin u| + (1/2)K

= (1/2) ln|sin 2x| + C, where C = (1/2)K is the integration constant.

Hence, we have proved that the integral of cot2x is equal to (1/2) ln |sin2x| + C.

We know that the cotangent function can be expressed as the ratio of the cosine function and the sine function. This implies cot2x can written as cot2x = cos2x/sin2x. Using this formula and the substitution method of integration, we can determine the integral of cot2x. Therefore, we have

∫cot2x dx = ∫(cos2x/sin2x) dx ---- (1)

Now, assume sin2x = t. Differentiating both sides, we have 2 cos2x dx = dt which implies cos2x dx = dt/2. Substituting these values in (1), we have

∫cot2x dx = ∫(1/t) (dt/2)

= (1/2) ∫(1/t) dt

= (1/2) ( ln |t| + K)

= (1/2) ln |sin2x| + (1/2)K

= (1/2) ln |sin2x| + C, where C = (1/2)K is the integration constant.

Next, in this article, we will evaluate the integral of cot square x. We know the trigonometric identity 1 + cot²x = cosec²x which implies cot²x = cosec²x -1. Using this formula of trigonometry, we can evaluate the integral of cot^2x. Also, we know that the derivative of cotx is -cosec²x which implies the integral of cosec²x is equal to -cotx + K. Using these facts and formulas of trigonometry, we have

∫cot^2x dx = ∫cot²x dx

= ∫(cosec²x -1) dx

= ∫cosec²x dx - ∫1 dx

= -cotx - x + C

Hence, the integral of cot^2x is equal to -cotx - x + C, where C is the integration constant.

Important Notes on Integral of Cot2x

• The integral of cot2x is given by, ∫cot2x dx = (1/2) ln |sin2x| + C, where C is the constant of integration.
• The integration of cot2x can be evaluated using the u-substitution method and using sin and cos.
• The integral of cot^2x is equal to -cotx - x + C.

☛ Related Topics:

• Cot Inverse x
• Derivative of Cotx
• Integration of Cotx

What is Integral of Cot2x in Calculus?

The integral of cot2x is equal to (1/2) ln |sin2x| + C, where C is the integration constant. We can calculate the integration cot2x using the u-substitution method. Mathematically, we can write the integral of cot2x as ∫cot2x dx = (1/2) ln |sin2x| + C.

How To Find the Integral of Cot2x?

The formula of the integration of cot2x can be determined using different integration formulas including the u-substitution method and expressing cot2x as the ratio of cos2x and sin2x.

What is the Integral of Cot Square x?

The integral of cot^2x is equal to -cotx - x + C, where C is the integration constant. We can find this integral of cot square x using the trigonometric identity 1 + cot²x = cosec²x.

Is the Antiderivative of Cot2x the Same as the Integral of Cot2x?

Antiderivative of a function is nothing but its integral as integration is the reverse process of differentiation (also known as antidifferentiation).

What is the Formula for The Integration of Cot2x?

The formula for the integration of cot2x is given by, ∫cot2x dx = (1/2) ln |sin2x| + C, where C is the constant of integration.

What is the Derivative of Cot2x?

The derivative of cot2x is given by, d(cot2x)/dx = -2 cosec²2x. We know the fact that the derivative of cotx is equal to -cosec²x. Using this formula and integration rules, we can determine the derivative of cot2x.