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Popular >

integral of 6/((x-2)^2)

Solution

\int \frac{6}{( x - 2 ) ^{2}} d x

Solution

- \frac{6}{x - 2} + C

Solution steps

\int \frac{6}{( x - 2 ) ^{2}} d x

Take the constant out:

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

= 6 \cdot \int \frac{1}{( x - 2 ) ^{2}} d x

Apply u-substitution

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

= 6 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 6 (- \frac{1}{u})

Substitute back

u = x - 2

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

Simplify

6 (- \frac{1}{x - 2}) : - \frac{6}{x - 2}

= - \frac{6}{x - 2}

Add a constant to the solution

= - \frac{6}{x - 2} + C

Graph

Popular Examples

integral of (8x(8-3x^2)^{1/3})/3

\int \frac{8 x ( 8 - 3 x ^{2} ) ^{\frac{1}{3}}}{3} d x

integral of-9/(9+x^2)

\int - \frac{9}{9 + x ^{2}} d x

integral of 6x^2(x^3+1)^{19}

\int 6 x^{2} (x^{3} + 1)^{19} d x

integral of (2x-1)ln(3x)

\int (2 x - 1) ln (3 x) d x

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

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

Frequently Asked Questions (FAQ)

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