What is the integral of 5/((3x-1)^3) ?

The integral of 5/((3x-1)^3) is -5/(6(3x-1)^2)+C

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integral of 5/((3x-1)^3)

\int \frac{5}{( 3 x - 1 ) ^{3}} d x

- \frac{5}{6 ( 3 x - 1 ) ^{2}} + C

Solution steps

\int \frac{5}{( 3 x - 1 ) ^{3}} d x

Take the constant out:

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

= 5 \cdot \int \frac{1}{( 3 x - 1 ) ^{3}} d x

Apply u-substitution

: \int \frac{1}{3 u ^{3}} d u

= 5 \cdot \int \frac{1}{3 u ^{3}} d u

Take the constant out:

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

= 5 \cdot \frac{1}{3} \cdot \int \frac{1}{u ^{3}} d u

Apply the Power Rule

: - \frac{1}{2 u ^{2}}

= 5 \cdot \frac{1}{3} (- \frac{1}{2 u ^{2}})

Substitute back

u = 3 x - 1

= 5 \cdot \frac{1}{3} (- \frac{1}{2 ( 3 x - 1 ) ^{2}})

Simplify

5 \cdot \frac{1}{3} (- \frac{1}{2 ( 3 x - 1 ) ^{2}}) : - \frac{5}{6 ( 3 x - 1 ) ^{2}}

= - \frac{5}{6 ( 3 x - 1 ) ^{2}}

Add a constant to the solution

= - \frac{5}{6 ( 3 x - 1 ) ^{2}} + C

\int \frac{e ^{- 5 x} + 3 x e ^{x}}{2} d x

x \to + 3 lim (\frac{1}{( x - 3 )})

y = 2 (12 x - 42)

2 t - \frac{8}{3}

z \to 0 lim (\frac{I m ( z )}{z})

What is the integral of 5/((3x-1)^3) ?
The integral of 5/((3x-1)^3) is -5/(6(3x-1)^2)+C