What is the integral of (5x^6+3x^5+5x^3+4-e^x) ?

The integral of (5x^6+3x^5+5x^3+4-e^x) is (5x^7)/7+(x^6)/2+(5x^4)/4+4x-e^x+C

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integral of (5x^6+3x^5+5x^3+4-e^x)

\int (5 x^{6} + 3 x^{5} + 5 x^{3} + 4 - e^{x}) d x

\frac{5 x ^{7}}{7} + \frac{x ^{6}}{2} + \frac{5 x ^{4}}{4} + 4 x - e^{x} + C

Solution steps

\int 5 x^{6} + 3 x^{5} + 5 x^{3} + 4 - 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 5 x^{6} d x + \int 3 x^{5} d x + \int 5 x^{3} d x + \int 4 d x - \int e^{x} d x

\int 5 x^{6} d x = \frac{5 x ^{7}}{7}

\int 3 x^{5} d x = \frac{x ^{6}}{2}

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

\int 4 d x = 4 x

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

= \frac{5 x ^{7}}{7} + \frac{x ^{6}}{2} + \frac{5 x ^{4}}{4} + 4 x - e^{x}

Add a constant to the solution

= \frac{5 x ^{7}}{7} + \frac{x ^{6}}{2} + \frac{5 x ^{4}}{4} + 4 x - e^{x} + C

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What is the integral of (5x^6+3x^5+5x^3+4-e^x) ?
The integral of (5x^6+3x^5+5x^3+4-e^x) is (5x^7)/7+(x^6)/2+(5x^4)/4+4x-e^x+C