What is the integral of x^4(x^3+8x^2+7) ?

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

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integral of x^4(x^3+8x^2+7)

\int x^{4} (x^{3} + 8 x^{2} + 7) d x

\frac{x ^{8}}{8} + \frac{8 x ^{7}}{7} + \frac{7 x ^{5}}{5} + C

Solution steps

\int x^{4} (x^{3} + 8 x^{2} + 7) d x

Expand

x^{4} (x^{3} + 8 x^{2} + 7) : x^{7} + 8 x^{6} + 7 x^{4}

= \int x^{7} + 8 x^{6} + 7 x^{4} 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 x^{7} d x + \int 8 x^{6} d x + \int 7 x^{4} d x

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

\int 8 x^{6} d x = \frac{8 x ^{7}}{7}

\int 7 x^{4} d x = \frac{7 x ^{5}}{5}

= \frac{x ^{8}}{8} + \frac{8 x ^{7}}{7} + \frac{7 x ^{5}}{5}

Add a constant to the solution

= \frac{x ^{8}}{8} + \frac{8 x ^{7}}{7} + \frac{7 x ^{5}}{5} + C

\frac{1}{2 x + 1}

\frac{\partial}{\partial x} (- \frac{1}{x ^{2} + y ^{2}})

f (x) = tan^{3} (x + csc (x))

y = 4 - x^{2}

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