What is the integral of (7x^2+5x+4) ?

The integral of (7x^2+5x+4) is (7x^3)/3+(5x^2)/2+4x+C

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integral of (7x^2+5x+4)

\int (7 x^{2} + 5 x + 4) d x

\frac{7 x ^{3}}{3} + \frac{5 x ^{2}}{2} + 4 x + C

Solution steps

\int 7 x^{2} + 5 x + 4 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 7 x^{2} d x + \int 5 x d x + \int 4 d x

\int 7 x^{2} d x = \frac{7 x ^{3}}{3}

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 4 d x = 4 x

= \frac{7 x ^{3}}{3} + \frac{5 x ^{2}}{2} + 4 x

Add a constant to the solution

= \frac{7 x ^{3}}{3} + \frac{5 x ^{2}}{2} + 4 x + C

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

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\int 7 x x^{2} - 1 d x

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

\int \frac{1}{( 2 x - 1 ) ( 2 x + 1 )} d x

What is the integral of (7x^2+5x+4) ?
The integral of (7x^2+5x+4) is (7x^3)/3+(5x^2)/2+4x+C