What is the integral of (10800)/(9q^2+675) ?

The integral of (10800)/(9q^2+675) is 80sqrt(3)arctan(1/(5sqrt(3))q)+C

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integral of (10800)/(9q^2+675)

\int \frac{10800}{9 q ^{2} + 675} d q

803 arctan (\frac{1}{5 3} q) + C

Solution steps

\int \frac{10800}{9 q ^{2} + 675} d q

Take the constant out:

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

= 10800 \cdot \int \frac{1}{9 q ^{2} + 675} d q

Apply Integral Substitution

= 10800 \cdot \int \frac{1}{45 3 ( u ^{2} + 1 )} d u

Take the constant out:

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

= 10800 \cdot \frac{1}{45 3} \cdot \int \frac{1}{u ^{2} + 1} d u

Use the common integral:

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

= 10800 \cdot \frac{1}{45 3} arctan (u)

Substitute back

u = \frac{3}{15 3} q

= 10800 \cdot \frac{1}{45 3} arctan (\frac{3}{15 3} q)

Simplify

10800 \cdot \frac{1}{45 3} arctan (\frac{3}{15 3} q) : 803 arctan (\frac{1}{5 3} q)

= 803 arctan (\frac{1}{5 3} q)

Add a constant to the solution

= 803 arctan (\frac{1}{5 3} q) + C

\int x sin (\frac{1}{3} x) d x

\frac{\partial}{\partial x} (z \cdot arctan (\frac{y}{x}))

y = x^{2}, (1, 1)

6 x - x^{2}

\frac{( 3 + 3 s )}{s ^{2} + 0.5}

What is the integral of (10800)/(9q^2+675) ?
The integral of (10800)/(9q^2+675) is 80sqrt(3)arctan(1/(5sqrt(3))q)+C