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Popular >

integral of x(3x+1)

Solution

\int x (3 x + 1) d x

Solution

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

Solution steps

\int x (3 x + 1) d x

Expand

x (3 x + 1) : 3 x^{2} + x

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

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

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

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

Add a constant to the solution

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

Popular Examples

sum from n=1 to infinity of cos^n(0.8)

n = 1 \sum \infty cos^{n} (0.8)

sum from n=0 to infinity of n(5/6)^{n-1}

n = 0 \sum \infty n (\frac{5}{6})^{n - 1}

derivative of x^2y+3x*y^3+x

\frac{d}{d x} (x^{2} y + 3 x \cdot y^{3} + x)

integral of cot(6x)

\int cot (6 x) d x

(\partial)/(\partial z)(x^3)

\frac{\partial}{\partial z} (x^{3})

Frequently Asked Questions (FAQ)

What is the integral of x(3x+1) ?
The integral of x(3x+1) is x^3+(x^2)/2+C