What is the integral of e+sec^2(θ)-e^θ ?

The integral of e+sec^2(θ)-e^θ is eθ+tan(θ)-e^θ+C

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integral of e+sec^2(θ)-e^θ

\int e + sec^{2} (θ) - e^{θ} d θ

e θ + tan (θ) - e^{θ} + C

Solution steps

\int e + sec^{2} (θ) - e^{θ} d θ

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int e d θ + \int sec^{2} (θ) d θ - \int e^{θ} d θ

\int e d θ = e θ

\int sec^{2} (θ) d θ = tan (θ)

\int e^{θ} d θ = e^{θ}

= e θ + tan (θ) - e^{θ}

Add a constant to the solution

= e θ + tan (θ) - e^{θ} + C

cot^{3} (4 x + 1)

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\int \frac{x ^{3}}{( 5 - x ^{4} ) ^{5}} d x

What is the integral of e+sec^2(θ)-e^θ ?
The integral of e+sec^2(θ)-e^θ is eθ+tan(θ)-e^θ+C