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

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

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integral of (4e^x)/(e^x+pi)

\int \frac{4 e ^{x}}{e ^{x} + π} d x

4 ln ∣ e^{x} + π ∣ + C

Solution steps

\int \frac{4 e ^{x}}{e ^{x} + π} 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} + π} 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} + π

= 4 ln ∣ e^{x} + π ∣

Add a constant to the solution

= 4 ln ∣ e^{x} + π ∣ + C

\frac{d}{d x} (x^{2} sin (x) + x)

f (x) = \frac{2}{x + 1}

\frac{( x ^{4} - 5 x ^{3} + x ^{\frac{1}{2}} )}{x ^{2}}

\int_{0}^{\infty} 4 x e^{- 2 x} d x

y^{^{''}} + 3 y^{^{'}} + 2 y = 4 t

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