What is the integral of x^5(3x^2+4) ?

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

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integral of x^5(3x^2+4)

\int x^{5} (3 x^{2} + 4) d x

\frac{3 x ^{8}}{8} + \frac{2 x ^{6}}{3} + C

Solution steps

\int x^{5} (3 x^{2} + 4) d x

Expand

x^{5} (3 x^{2} + 4) : 3 x^{7} + 4 x^{5}

= \int 3 x^{7} + 4 x^{5} 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 3 x^{7} d x + \int 4 x^{5} d x

\int 3 x^{7} d x = \frac{3 x ^{8}}{8}

\int 4 x^{5} d x = \frac{2 x ^{6}}{3}

= \frac{3 x ^{8}}{8} + \frac{2 x ^{6}}{3}

Add a constant to the solution

= \frac{3 x ^{8}}{8} + \frac{2 x ^{6}}{3} + C

\frac{d}{d x} (ln (tan (x^{2})))

\frac{d}{d x} (arctan (x) + x - 1)

y^{^{''}} - 16 y^{^{'}} + 73 = 0, y (0) = 6, y^{^{'}} (0) = 6

\frac{d}{d x} (\frac{1}{2} (4 x^{2} + x)^{- 3})

y^{^{'}} = - 3 y

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