What is the integral of (300)/((2x+1))+12x^3-8x ?

The integral of (300)/((2x+1))+12x^3-8x is 150ln|2x+1|+3x^4-4x^2+C

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integral of (300)/((2x+1))+12x^3-8x

integral

\frac{300}{( 2 x + 1 )} + 12 x^{3} - 8 x

150 ln ∣ 2 x + 1 ∣ + 3 x^{4} - 4 x^{2} + C

Solution steps

\int \frac{300}{2 x + 1} + 12 x^{3} - 8 x 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{300}{2 x + 1} d x + \int 12 x^{3} d x - \int 8 x d x

\int \frac{300}{2 x + 1} d x = 150 ln ∣ 2 x + 1 ∣

\int 12 x^{3} d x = 3 x^{4}

\int 8 x d x = 4 x^{2}

= 150 ln ∣ 2 x + 1 ∣ + 3 x^{4} - 4 x^{2}

Add a constant to the solution

= 150 ln ∣ 2 x + 1 ∣ + 3 x^{4} - 4 x^{2} + C

What is the integral of (300)/((2x+1))+12x^3-8x ?
The integral of (300)/((2x+1))+12x^3-8x is 150ln|2x+1|+3x^4-4x^2+C