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

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

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

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

ln x^{3} + e^{x} + C

Solution steps

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

Apply u-substitution

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x^{3} + e^{x}

= ln x^{3} + e^{x}

Add a constant to the solution

= ln x^{3} + e^{x} + C

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