What is the integral of c/(1+y^2) ?

The integral of c/(1+y^2) is carctan(y)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of c/(1+y^2)

\int \frac{c}{1 + y ^{2}} d y

c arctan (y) + C

Solution steps

\int \frac{c}{1 + y ^{2}} d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= c \cdot \int \frac{1}{1 + y ^{2}} d y

Use the common integral:

\int \frac{1}{1 + y ^{2}} d y = arctan (y)

= c arctan (y)

Add a constant to the solution

= c arctan (y) + C

\int ln (x) \cdot x^{4} d x

\int \frac{5}{x ln ( x ^{3} )} d x

\int \frac{1}{2 ( x - 3 ) ^{2} + 1} d x

\int x x + \frac{1}{x ^{3}} d x

\int \frac{1}{x} \cdot \frac{1}{ln ( x )} d x