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Popular >

integral of x(x^5+3)

Solution

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

Solution

\frac{x ^{7}}{7} + \frac{3 x ^{2}}{2} + C

Solution steps

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

Expand

x (x^{5} + 3) : x^{6} + 3 x

= \int x^{6} + 3 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 x^{6} d x + \int 3 x d x

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

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

= \frac{x ^{7}}{7} + \frac{3 x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{7}}{7} + \frac{3 x ^{2}}{2} + C

Popular Examples

derivative of y=(x^2+8)^2-4x derivative of

y = (x^{2} + 8)^{2} - 4 x

(\partial)/(\partial x)(9csc(6x^4-9x+5))

\frac{\partial}{\partial x} (9 csc (6 x^{4} - 9 x + 5))

implicit (dy)/(dx),e^{x/y}=6x-y implicit derivative

\frac{d y}{d x}, e^{\frac{x}{y}} = 6 x - y

derivative of 8/((1-2x^3))

\frac{d}{d x} (\frac{8}{( 1 - 2 x ) ^{3}})

derivative of (x^5/(10))

\frac{d}{d x} (\frac{x ^{5}}{10})

Frequently Asked Questions (FAQ)

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