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

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

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integral of (4e^x)/(e^x+sqrt(3))

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

4 ln e^{x} + 3 + C

Solution steps

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

Take the constant out:

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

= 4 \cdot \int \frac{e ^{x}}{e ^{x} + 3} d x

Apply u-substitution

= 4 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 4 ln ∣ u ∣

Substitute back

u = e^{x} + 3

= 4 ln e^{x} + 3

Add a constant to the solution

= 4 ln e^{x} + 3 + C

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