What is the integral of e^x+x^e+e+x ?

The integral of e^x+x^e+e+x is e^x+(x^{e+1}}{e+1}+ex+\frac{x^2)/2+C

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integral of e^x+x^e+e+x

\int e^{x} + x^{e} + e + x d x

e^{x} + \frac{x ^{e + 1}}{e + 1} + e x + \frac{x ^{2}}{2} + C

Solution steps

\int e^{x} + x^{e} + e + x d x

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^{x} d x + \int x^{e} d x + \int e d x + \int x d x

\int e^{x} d x = e^{x}

\int x^{e} d x = \frac{x ^{e + 1}}{e + 1}

\int e d x = e x

\int x d x = \frac{x ^{2}}{2}

= e^{x} + \frac{x ^{e + 1}}{e + 1} + e x + \frac{x ^{2}}{2}

Add a constant to the solution

= e^{x} + \frac{x ^{e + 1}}{e + 1} + e x + \frac{x ^{2}}{2} + C

f (x) = sin (4 x) - cos (3 x)

\frac{d y}{d x} = x^{3} + x^{2} - 5 x + 11

\int_{1}^{1000} \frac{21}{x ^{3}} d x

y^{^{''}} - 2 y^{^{'}} + 5 y = e^{t} cos (2 t)

(sin (6 t) - 7)^{2}

What is the integral of e^x+x^e+e+x ?
The integral of e^x+x^e+e+x is e^x+(x^{e+1}}{e+1}+ex+\frac{x^2)/2+C