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Popular >

integral of x(15x+6)

Solution

\int x (15 x + 6) d x

Solution

5 x^{3} + 3 x^{2} + C

Solution steps

\int x (15 x + 6) d x

Expand

x (15 x + 6) : 15 x^{2} + 6 x

= \int 15 x^{2} + 6 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 15 x^{2} d x + \int 6 x d x

\int 15 x^{2} d x = 5 x^{3}

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

= 5 x^{3} + 3 x^{2}

Add a constant to the solution

= 5 x^{3} + 3 x^{2} + C

Popular Examples

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derivative of (5x/(7x^2+1))

\frac{d}{d x} (\frac{5 x}{7 x ^{2} + 1})

y^{^{''}} + a y = 0

Frequently Asked Questions (FAQ)

What is the integral of x(15x+6) ?
The integral of x(15x+6) is 5x^3+3x^2+C