What is the integral of 1/((D*E)-(D*F/G x)) ?

The integral of 1/((D*E)-(D*F/G x)) is -G/(DF)ln|DE-F/G Dx|+C

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integral of 1/((DE)-(DF/G x))

\int \frac{1}{( D \cdot E ) - ( D \cdot \frac{F}{G} x )} d x

- \frac{G}{D F} ln D E - \frac{F}{G} D x + C

Solution steps

\int \frac{1}{D E - D \frac{F}{G} x} d x

Apply u-substitution

: \int - \frac{G}{D F u} d u

= \int - \frac{G}{D F u} d u

Take the constant out:

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

= - \frac{G}{D F} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{G}{D F} ln ∣ u ∣

Substitute back

u = D E - \frac{F}{G} D x

= - \frac{G}{D F} ln D E - \frac{F}{G} D x

Add a constant to the solution

= - \frac{G}{D F} ln D E - \frac{F}{G} D x + C

\frac{d}{d x} ((- 2 x^{3} + 2 x^{2})^{4})

\frac{d}{d x} ((x + 2)^{- 1})

\frac{2 s + 3}{s ^{2} - 4 s + 20}

f (x) = x^{2} (1 - 2 x)

\frac{d y}{d x} = \frac{5 x}{y}

What is the integral of 1/((D*E)-(D*F/G x)) ?
The integral of 1/((D*E)-(D*F/G x)) is -G/(DF)ln|DE-F/G Dx|+C