What is the integral of (2x-5)/7 ?

The integral of (2x-5)/7 is 1/7 (x^2-5x)+C

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integral of (2x-5)/7

\int \frac{2 x - 5}{7} d x

\frac{1}{7} (x^{2} - 5 x) + C

Solution steps

\int \frac{2 x - 5}{7} d x

Take the constant out:

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

= \frac{1}{7} \cdot \int 2 x - 5 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

= \frac{1}{7} (\int 2 x d x - \int 5 d x)

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

\int 5 d x = 5 x

= \frac{1}{7} (x^{2} - 5 x)

Add a constant to the solution

= \frac{1}{7} (x^{2} - 5 x) + C

7 y^{^{''}} + 27 y = 0, y (0) = 6, y^{^{'}} (0) = 5

\int - 5 x^{- 6} d x

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

\int \frac{1}{x ^{2} - x ^{4}} d x

5 x^{3} - x^{2} y + y^{3} + 1 = 0, (1, - 2)