What is the integral of (3x-2)^{-11} ?

The integral of (3x-2)^{-11} is -1/(30(3x-2)^{10)}+C

Popular >

integral of (3x-2)^{-11}

\int (3 x - 2)^{- 11} d x

- \frac{1}{30 ( 3 x - 2 ) ^{10}} + C

Solution steps

\int (3 x - 2)^{- 11} d x

Apply u-substitution

: \int \frac{1}{3 u ^{11}} d u

= \int \frac{1}{3 u ^{11}} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int \frac{1}{u ^{11}} d u

Apply the Power Rule

: - \frac{1}{10 u ^{10}}

= \frac{1}{3} (- \frac{1}{10 u ^{10}})

Substitute back

u = 3 x - 2

= \frac{1}{3} (- \frac{1}{10 ( 3 x - 2 ) ^{10}})

Simplify

\frac{1}{3} (- \frac{1}{10 ( 3 x - 2 ) ^{10}}) : - \frac{1}{30 ( 3 x - 2 ) ^{10}}

= - \frac{1}{30 ( 3 x - 2 ) ^{10}}

Add a constant to the solution

= - \frac{1}{30 ( 3 x - 2 ) ^{10}} + C

n = 1 \sum \infty \frac{2}{n ( n + 3 )}

x \to 5 lim (4 x - 3 x^{2})

x \to 5 lim (x^{2} + 2 x - 35)

y = 3 csc^{2} (5 x)^{3}

f (x) = x^{3} + 3 x^{2} - 45 x - 19

What is the integral of (3x-2)^{-11} ?
The integral of (3x-2)^{-11} is -1/(30(3x-2)^{10)}+C