What is the integral of 5/(1+5t^2) ?

The integral of 5/(1+5t^2) is sqrt(5)arctan(sqrt(5)t)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5/(1+5t^2)

\int \frac{5}{1 + 5 t ^{2}} d t

5 arctan (5 t) + C

Solution steps

\int \frac{5}{1 + 5 t ^{2}} d t

Take the constant out:

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

= 5 \cdot \int \frac{1}{1 + 5 t ^{2}} d t

Apply Integral Substitution

= 5 \cdot \int \frac{1}{5 ( 1 + u ^{2} )} d u

Take the constant out:

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

= 5 \cdot \frac{1}{5} \cdot \int \frac{1}{1 + u ^{2}} d u

Use the common integral:

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

= 5 \cdot \frac{1}{5} arctan (u)

Substitute back

u = 5 t

= 5 \cdot \frac{1}{5} arctan (5 t)

Simplify

5 \cdot \frac{1}{5} arctan (5 t) : 5 arctan (5 t)

= 5 arctan (5 t)

Add a constant to the solution

= 5 arctan (5 t) + C

\int t t + 3 d t

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

\int 2 x arcsin (x^{2}) d x

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

\int \frac{( x + 1 )}{( x ^{2} - 2 x + 5 )} d x

What is the integral of 5/(1+5t^2) ?
The integral of 5/(1+5t^2) is sqrt(5)arctan(sqrt(5)t)+C