What is the integral of ((4-ln|x+3|)^3)/(x+3) ?

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

Popular >

integral of ((4-ln|x+3|)^3)/(x+3)

\int \frac{( 4 - ln ∣ x + 3 ∣ ) ^{3}}{x + 3} d x

- \frac{( 4 - ln ∣ x + 3 ∣ ) ^{4}}{4} + C

Solution steps

\int \frac{( 4 - ln ∣ x + 3 ∣ ) ^{3}}{x + 3} d x

Apply u-substitution

: \int - u^{3} d u

= \int - u^{3} d u

Take the constant out:

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

= - \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= - \frac{u ^{4}}{4}

Substitute back

u = 4 - ln ∣ x + 3 ∣

= - \frac{( 4 - ln ∣ x + 3 ∣ ) ^{4}}{4}

Add a constant to the solution

= - \frac{( 4 - ln ∣ x + 3 ∣ ) ^{4}}{4} + C

\frac{d}{d x} (x^{2} \cdot e^{- x})

\int_{0}^{1} x 3^{x} d x

25 - 5 x ln (0.04 x) - x

x \to 0 + lim (- 4 csc^{2} (4 x))

\int \frac{x - 4}{x ^{2} - x - 6} d x

What is the integral of ((4-ln|x+3|)^3)/(x+3) ?
The integral of ((4-ln|x+3|)^3)/(x+3) is -((4-ln|x+3|)^4)/4+C