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Popular >

integral of (1+3x)^2

Solution

\int (1 + 3 x)^{2} d x

Solution

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

Solution steps

\int (1 + 3 x)^{2} d x

Expand

(1 + 3 x)^{2} : 1 + 6 x + 9 x^{2}

= \int 1 + 6 x + 9 x^{2} 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 1 d x + \int 6 x d x + \int 9 x^{2} d x

\int 1 d x = x

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

\int 9 x^{2} d x = 3 x^{3}

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

Add a constant to the solution

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

Popular Examples

sum from n=1 to infinity of arctan(15n)

n = 1 \sum \infty arctan (15 n)

tangent of f(x)=6x^2+6,\at x=-2 tangent of

f (x) = 6 x^{2} + 6, at x = - 2

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(3 x - 1) (x - 2)^{4}

integral of (x^2)/(sqrt(x^2+18))

\int \frac{x ^{2}}{x ^{2} + 18} d x

limit as x approaches 3 of (x-4)/(x^2-9)

x \to 3 lim (\frac{x - 4}{x ^{2} - 9})

Frequently Asked Questions (FAQ)

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