What is the integral of 8(x^7+7^x+7x+7) ?

The integral of 8(x^7+7^x+7x+7) is x^8+(8*7^x)/(ln(7))+28x^2+56x+C

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integral of 8(x^7+7^x+7x+7)

\int 8 (x^{7} + 7^{x} + 7 x + 7) d x

x^{8} + \frac{8 \cdot 7 ^{x}}{ln ( 7 )} + 28 x^{2} + 56 x + C

Solution steps

\int 8 (x^{7} + 7^{x} + 7 x + 7) d x

Take the constant out:

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

= 8 \cdot \int x^{7} + 7^{x} + 7 x + 7 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

= 8 (\int x^{7} d x + \int 7^{x} d x + \int 7 x d x + \int 7 d x)

\int x^{7} d x = \frac{x ^{8}}{8}

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

\int 7 x d x = \frac{7 x ^{2}}{2}

\int 7 d x = 7 x

= 8 (\frac{x ^{8}}{8} + \frac{7 ^{x}}{ln ( 7 )} + \frac{7 x ^{2}}{2} + 7 x)

Simplify

8 (\frac{x ^{8}}{8} + \frac{7 ^{x}}{ln ( 7 )} + \frac{7 x ^{2}}{2} + 7 x) : x^{8} + \frac{8 \cdot 7 ^{x}}{ln ( 7 )} + 28 x^{2} + 56 x

= x^{8} + \frac{8 \cdot 7 ^{x}}{ln ( 7 )} + 28 x^{2} + 56 x

Add a constant to the solution

= x^{8} + \frac{8 \cdot 7 ^{x}}{ln ( 7 )} + 28 x^{2} + 56 x + C

What is the integral of 8(x^7+7^x+7x+7) ?
The integral of 8(x^7+7^x+7x+7) is x^8+(8*7^x)/(ln(7))+28x^2+56x+C