What is the integral of 90x+(500)/(1+x) ?

The integral of 90x+(500)/(1+x) is 45x^2+500ln|1+x|+C

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integral of 90x+(500)/(1+x)

\int 90 x + \frac{500}{1 + x} d x

45 x^{2} + 500 ln ∣ 1 + x ∣ + C

Solution steps

\int 90 x + \frac{500}{1 + 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 90 x d x + \int \frac{500}{1 + x} d x

\int 90 x d x = 45 x^{2}

\int \frac{500}{1 + x} d x = 500 ln ∣ 1 + x ∣

= 45 x^{2} + 500 ln ∣ 1 + x ∣

Add a constant to the solution

= 45 x^{2} + 500 ln ∣ 1 + x ∣ + C

What is the integral of 90x+(500)/(1+x) ?
The integral of 90x+(500)/(1+x) is 45x^2+500ln|1+x|+C