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

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

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

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

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

Solution steps

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

\int 2 x^{4} d x = \frac{2 x ^{5}}{5}

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

\int \frac{x ^{2} - 2 x + 5}{x - 3} d x

\int \frac{y}{y ^{2} + 3} d y

\int x^{2} \frac{1}{1 + x ^{2}} d x

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

\int 4 x cos^{2} (x) d x

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