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

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

Popular >

integral of (e^x+sec^2(x))/(e^x+tan(x))

\int \frac{e ^{x} + sec ^{2} ( x )}{e ^{x} + tan ( x )} d x

ln ∣ e^{x} + tan (x) ∣ + C

Solution steps

\int \frac{e ^{x} + sec ^{2} ( x )}{e ^{x} + tan ( x )} d x

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = e^{x} + tan (x)

= ln ∣ e^{x} + tan (x) ∣

Add a constant to the solution

= ln ∣ e^{x} + tan (x) ∣ + C

\frac{s - 4}{( s ^{2} + 5 ) ^{2}}

\int_{0}^{4} x x^{2} + 9 d x

\int \frac{1}{x ^{4} x ^{2} + 3} d x

x \to 0 lim (\frac{x ^{3}}{x ^{4}})

y = 5 x^{2}, (- 2, 20)

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