What is the integral of (7x^3-2x^2+4) ?

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

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integral of (7x^3-2x^2+4)

\int (7 x^{3} - 2 x^{2} + 4) d x

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

Solution steps

\int 7 x^{3} - 2 x^{2} + 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^{3} d x - \int 2 x^{2} d x + \int 4 d x

\int 7 x^{3} d x = \frac{7 x ^{4}}{4}

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

\int 4 d x = 4 x

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

Add a constant to the solution

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

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y^{^{''}} + 2 y^{^{'}} + y = 0, y (1) = 1, y^{^{'}} (1) = 0

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