- ∫g'(x)g(x)dx=ln|g(x)|+C. (You can verify this by substitution u=g(x) .) Now, let us look at the posted antiderivative.
- By the trig identity tanx=sinxcosx ,
- ∫tanxdx=∫sinxcosxdx. by rewriting it a bit further to fit the form above,
- =−∫−sinxcosxdx. by the formula above, …
- or by rlnx=lnxr , =ln|cosx|−1+C=ln|secx|+C.

## What is the antiderivative of Sinx?

What is the antiderivative of sin. A lot of people just memorize that the antiderivative of sinx is simply –**cosx**.

## Is integral of TANX improper?

dx x2 − 1 is an improper integral of **type 2** because 1 x2 − 1 is not continuous at −1 and 1. tan xdx is an improper integral of type 2 because tan x is not continuous at π 2 . … If either the lower limit of integration, the upper limit of integration or both are not finite, it will be an improper integral of type 1.

## What is the antiderivative of Secx?

The antiderivative of sec(x) is **ln |secx + tanx| + C**, where C is a constant.

### What is secX equal to?

The secant of x is 1 divided by the cosine of x: **sec x = 1 cos x** , and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x .

### How do you find the antiderivative?

To find an antiderivative for a function f, we can often **reverse the process of differentiation**. For example, if f = x^{4}, then an antiderivative of f is F = x^{5}, which can be found by reversing the power rule. Notice that not only is x^{5} an antiderivative of f, but so are x^{5} + 4, x^{5} + 6, etc.

### What is the integration of tan 2x?

The integral of tan 2x is **(-1/2) ln |cos 2x| + C or (1/2) ln |sec 2x| + C**.

### What is the graph of TANX?

Graphing y = tan x

Unlike the sine and cosine functions, the tangent function is π periodic. That is, if the point (x, y) lies on the graph of y = tan x so will the point **(x + kπ , y)** where k is any integer.

### What is the differentiation of tan theta?

The formula for differentiation of tan x is, **d/dx (tan x) = sec ^{2}x (or)**

### What is the antiderivative calculator?

Antiderivative Calculator is **a free online tool that displays the antiderivative (integration) of a given function**. BYJU’S online antiderivative calculator tool makes the calculation faster, and it displays the integrated value in a fraction of seconds.

### What is the antiderivative of 0?

When speaking of indefinite integrals, the integral of 0 is just 0 plus the usual arbitrary constant, i.e., derivative. / | | 0 dx = 0 + C = C | / **There’s no contradiction here**.

### What is Arctan formula?

In trigonometry, arctan is the inverse of the tangent function and is used to compute the angle measure from the tangent ratio (tan = opposite/adjacent) of a right triangle. Arctan can be calculated in terms of degrees and as well as radians. $large arctan (x)=2arctan left ( **frac{x}{1+sqrt{1+x^{2**}}} right )$

### What is CSC formula?

For example, csc A = **1/sin A**, sec A = 1/cos A, cot A = 1/tan A, and tan A = sin A/cos A.

### What is the derivative of tan theta by 2?

Answer: The derivative of y = tan^{2}x is **dy/dx = 2 sec ^{2}x tan x**. Let us proceed for this problem step by step. Explanation: We can proceed by using chain rule.

### What is dy dx?

dy/dx is basically **another way of writing y’** and is used a lot in integral calculus. dy/dx is said to be taking the derivative of y with respect to x (sort of like ‘solve for y in terms of x’ – type terminology). So dy/dt would be taking the derivative of y with respect to t where t is your independent variable.

### What is integration in simple words?

1 : the **act or process of uniting different things**. 2 : the practice of uniting people from different races in an attempt to give people equal rights racial integration. integration. noun.