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

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

= 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

\frac{d}{d x} (x^{\frac{4}{5}} (x - 4)^{2})

x y + y^{2} - x^{2} \frac{d y}{d x} = 0

\int_{1}^{2} 11 4 x^{2} - 3 d x

\frac{1}{( s ^{2} + 1 ) ( s ^{2} - 6 )}

f (x) = (e^{x} + 1)^{7 x}

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