What is the integral of 4/((x+3)^2) ?

The integral of 4/((x+3)^2) is -4/(x+3)+C

Popular >

integral of 4/((x+3)^2)

\int \frac{4}{( x + 3 ) ^{2}} d x

- \frac{4}{x + 3} + C

Solution steps

\int \frac{4}{( x + 3 ) ^{2}} d x

Take the constant out:

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

= 4 \cdot \int \frac{1}{( x + 3 ) ^{2}} d x

Apply u-substitution

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

= 4 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 4 (- \frac{1}{u})

Substitute back

u = x + 3

= 4 (- \frac{1}{x + 3})

Simplify

4 (- \frac{1}{x + 3}) : - \frac{4}{x + 3}

= - \frac{4}{x + 3}

Add a constant to the solution

= - \frac{4}{x + 3} + C

\frac{\partial}{\partial y} (x^{3} y^{10} sin (x y^{2}))

\int 6 t e^{3 t} d t

x \to 0 lim (\frac{x ^{3}}{x ^{3}})

\frac{d}{d x} (a^{2} sin^{2} (x))

f (x) = \frac{x}{x + 3}, at x = - 2