What is the integral of (900)/((2q-5)^2) ?

The integral of (900)/((2q-5)^2) is -(450)/(2q-5)+C

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integral of (900)/((2q-5)^2)

\int \frac{900}{( 2 q - 5 ) ^{2}} d q

- \frac{450}{2 q - 5} + C

Solution steps

\int \frac{900}{( 2 q - 5 ) ^{2}} d q

Take the constant out:

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

= 900 \cdot \int \frac{1}{( 2 q - 5 ) ^{2}} d q

Apply u-substitution

: \int \frac{1}{2 u ^{2}} d u

= 900 \cdot \int \frac{1}{2 u ^{2}} d u

Take the constant out:

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

= 900 \cdot \frac{1}{2} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 900 \cdot \frac{1}{2} (- \frac{1}{u})

Substitute back

u = 2 q - 5

= 900 \cdot \frac{1}{2} (- \frac{1}{2 q - 5})

Simplify

900 \cdot \frac{1}{2} (- \frac{1}{2 q - 5}) : - \frac{450}{2 q - 5}

= - \frac{450}{2 q - 5}

Add a constant to the solution

= - \frac{450}{2 q - 5} + C

\frac{d}{d x} (\frac{5}{3} x^{2})

x \to 0 lim (x \cdot sin (x))

\int_{1}^{\infty} 15 e^{- 5 x} d x

\frac{d}{d x} (cos (2 x) + x^{2})

f (x) = (1 - x^{3}) + (1 - x^{3})

What is the integral of (900)/((2q-5)^2) ?
The integral of (900)/((2q-5)^2) is -(450)/(2q-5)+C