What is the integral of (15)/(1+9x^2) ?

The integral of (15)/(1+9x^2) is 5arctan(3x)+C

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integral of (15)/(1+9x^2)

\int \frac{15}{1 + 9 x ^{2}} d x

5 arctan (3 x) + C

Solution steps

\int \frac{15}{1 + 9 x ^{2}} d x

Take the constant out:

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

= 15 \cdot \int \frac{1}{1 + 9 x ^{2}} d x

Apply Integral Substitution

= 15 \cdot \int \frac{1}{3 ( 1 + u ^{2} )} d u

Take the constant out:

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

= 15 \cdot \frac{1}{3} \cdot \int \frac{1}{1 + u ^{2}} d u

Use the common integral:

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

= 15 \cdot \frac{1}{3} arctan (u)

Substitute back

u = 3 x

= 15 \cdot \frac{1}{3} arctan (3 x)

Simplify

15 \cdot \frac{1}{3} arctan (3 x) : 5 arctan (3 x)

= 5 arctan (3 x)

Add a constant to the solution

= 5 arctan (3 x) + C

- 4 x + x^{2} + 10, 9 - 2 x, 2 x + 1

y = x - 2 3 x

\frac{d P}{d t} = P - P^{2}

(2) (e^{3 x})

\frac{d y}{d x}, x^{2} + x y + y^{2} = 7

What is the integral of (15)/(1+9x^2) ?
The integral of (15)/(1+9x^2) is 5arctan(3x)+C