What is the integral of (x^{10}+10^x)/(10) ?

The integral of (x^{10}+10^x)/(10) is 1/10 ((x^{11})/(11)+(10^x)/(ln(10)))+C

integral of (x^{10}+10^x)/(10)

\int \frac{x ^{10} + 1 0 ^{x}}{10} d x

\frac{1}{10} (\frac{x ^{11}}{11} + \frac{1 0 ^{x}}{ln ( 10 )}) + C

Solution steps

\int \frac{x ^{10} + 1 0 ^{x}}{10} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{10} \cdot \int x^{10} + 1 0^{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

= \frac{1}{10} (\int x^{10} d x + \int 1 0^{x} d x)

\int x^{10} d x = \frac{x ^{11}}{11}

\int 1 0^{x} d x = \frac{1 0 ^{x}}{ln ( 10 )}

= \frac{1}{10} (\frac{x ^{11}}{11} + \frac{1 0 ^{x}}{ln ( 10 )})

Add a constant to the solution

= \frac{1}{10} (\frac{x ^{11}}{11} + \frac{1 0 ^{x}}{ln ( 10 )}) + C

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What is the integral of (x^{10}+10^x)/(10) ?
The integral of (x^{10}+10^x)/(10) is 1/10 ((x^{11})/(11)+(10^x)/(ln(10)))+C