What is the integral of (e^x+x^e+ex+c/x+7^x) ?

The integral of (e^x+x^e+ex+c/x+7^x) is e^x+(x^{e+1}}{e+1}+(ex^2)/2+cln|x|+\frac{7^x)/(ln(7))+C

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integral of (e^x+x^e+ex+c/x+7^x)

\int (e^{x} + x^{e} + e x + \frac{c}{x} + 7^{x}) d x

e^{x} + \frac{x ^{e + 1}}{e + 1} + \frac{e x ^{2}}{2} + c ln ∣ x ∣ + \frac{7 ^{x}}{ln ( 7 )} + C

Solution steps

\int e^{x} + x^{e} + e x + \frac{c}{x} + 7^{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 x d x + \int \frac{c}{x} d x + \int 7^{x} d x

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

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

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

\int \frac{c}{x} d x = c ln ∣ x ∣

\int 7^{x} d x = \frac{7 ^{x}}{ln ( 7 )}

= e^{x} + \frac{x ^{e + 1}}{e + 1} + \frac{e x ^{2}}{2} + c ln ∣ x ∣ + \frac{7 ^{x}}{ln ( 7 )}

Add a constant to the solution

= e^{x} + \frac{x ^{e + 1}}{e + 1} + \frac{e x ^{2}}{2} + c ln ∣ x ∣ + \frac{7 ^{x}}{ln ( 7 )} + C

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What is the integral of (e^x+x^e+ex+c/x+7^x) ?
The integral of (e^x+x^e+ex+c/x+7^x) is e^x+(x^{e+1}}{e+1}+(ex^2)/2+cln|x|+\frac{7^x)/(ln(7))+C