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

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

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integral of x-2+3/((3x-5)^6)

\int x - 2 + \frac{3}{( 3 x - 5 ) ^{6}} d x

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

Solution steps

\int x - 2 + \frac{3}{( 3 x - 5 ) ^{6}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x d x - \int 2 d x + \int \frac{3}{( 3 x - 5 ) ^{6}} d x

\int x d x = \frac{x ^{2}}{2}

\int 2 d x = 2 x

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

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

Add a constant to the solution

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

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