What is the integral of (4+3x^2)/(x^3+4x) ?

The integral of (4+3x^2)/(x^3+4x) is ln|x|+ln|x^2+4|+C

Popular >

integral of (4+3x^2)/(x^3+4x)

\int \frac{4 + 3 x ^{2}}{x ^{3} + 4 x} d x

ln ∣ x ∣ + ln x^{2} + 4 + C

Solution steps

\int \frac{4 + 3 x ^{2}}{x ^{3} + 4 x} d x

Take the partial fraction of

\frac{4 + 3 x ^{2}}{x ^{3} + 4 x} : \frac{1}{x} + \frac{2 x}{x ^{2} + 4}

= \int \frac{1}{x} + \frac{2 x}{x ^{2} + 4} 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 \frac{1}{x} d x + \int \frac{2 x}{x ^{2} + 4} d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{2 x}{x ^{2} + 4} d x = ln x^{2} + 4

= ln ∣ x ∣ + ln x^{2} + 4

Add a constant to the solution

= ln ∣ x ∣ + ln x^{2} + 4 + C

\int 2 x 3 - 2 x^{2} d x

\int - 5 x + 10 - e^{- x} d x

\int (1 + sin^{2} (θ) csc (θ)) d θ

\int \frac{x ^{3}}{x ^{2} + 22 x + 121} d x

\int \frac{2}{( t + 3 ) t ^{2} + 6 t - 7} d t

What is the integral of (4+3x^2)/(x^3+4x) ?
The integral of (4+3x^2)/(x^3+4x) is ln|x|+ln|x^2+4|+C