What is the integral of 3/((x+3)^2) ?

The integral of 3/((x+3)^2) is -3/(x+3)+C

Popular >

integral of 3/((x+3)^2)

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

- \frac{3}{x + 3} + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

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

Apply the Power Rule

: - \frac{1}{u}

= 3 (- \frac{1}{u})

Substitute back

u = x + 3

= 3 (- \frac{1}{x + 3})

Simplify

3 (- \frac{1}{x + 3}) : - \frac{3}{x + 3}

= - \frac{3}{x + 3}

Add a constant to the solution

= - \frac{3}{x + 3} + C

f (x) = 3^{x^{2} - x + 5}

\frac{d y}{d x} + 7 = e^{7 x + y - 5}

\int \frac{5}{x 25 - ( ln ( x ) ) ^{2}} d x

\int cos (x) e^{- 3 x} d x

y = \frac{x}{25 + x ^{2}}, (0, 0)