What is the integral of (5x^6-8x^3+5x+9) ?

The integral of (5x^6-8x^3+5x+9) is (5x^7)/7-2x^4+(5x^2)/2+9x+C

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integral of (5x^6-8x^3+5x+9)

\int (5 x^{6} - 8 x^{3} + 5 x + 9) d x

\frac{5 x ^{7}}{7} - 2 x^{4} + \frac{5 x ^{2}}{2} + 9 x + C

Solution steps

\int 5 x^{6} - 8 x^{3} + 5 x + 9 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 8 x^{3} d x + \int 5 x d x + \int 9 d x

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

\int 8 x^{3} d x = 2 x^{4}

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

\int 9 d x = 9 x

= \frac{5 x ^{7}}{7} - 2 x^{4} + \frac{5 x ^{2}}{2} + 9 x

Add a constant to the solution

= \frac{5 x ^{7}}{7} - 2 x^{4} + \frac{5 x ^{2}}{2} + 9 x + C

\int \frac{x + 4}{x ^{2} + 5 x + 6} d x

\int \frac{4 s}{( 1 - 2 s ^{2} ) ^{2}} d s

\int e^{t a n (x^{2})} \cdot x \cdot sec^{2} (x^{2}) d x

What is the integral of (5x^6-8x^3+5x+9) ?
The integral of (5x^6-8x^3+5x+9) is (5x^7)/7-2x^4+(5x^2)/2+9x+C