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Popular >

integral of (3x+7)^2

Solution

\int (3 x + 7)^{2} d x

Solution

3 x^{3} + 21 x^{2} + 49 x + C

Solution steps

\int (3 x + 7)^{2} d x

Expand

(3 x + 7)^{2} : 9 x^{2} + 42 x + 49

= \int 9 x^{2} + 42 x + 49 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 9 x^{2} d x + \int 42 x d x + \int 49 d x

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

\int 42 x d x = 21 x^{2}

\int 49 d x = 49 x

= 3 x^{3} + 21 x^{2} + 49 x

Add a constant to the solution

= 3 x^{3} + 21 x^{2} + 49 x + C

Graph

Popular Examples

integral of (3/91)x^2

\int (\frac{3}{91}) x^{2} d x

integral of (x^2-3)/(x-x^3)

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

integral of x/((x^2-5)^{1/7)}

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

integral of 8sqrt(1+x^4)

\int 8 1 + x^{4} d x

integral of (4x+5)/(x^2-11x+30)

\int \frac{4 x + 5}{x ^{2} - 11 x + 30} d x

Frequently Asked Questions (FAQ)

What is the integral of (3x+7)^2 ?
The integral of (3x+7)^2 is 3x^3+21x^2+49x+C