What is the integral of (3x-1x-7ex+14e) ?

The integral of (3x-1x-7ex+14e) is (3x^2)/2-(x^2)/2-(7ex^2)/2+14ex+C

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integral of (3x-1x-7ex+14e)

\int (3 x - 1 x - 7 e x + 14 e) d x

\frac{3 x ^{2}}{2} - \frac{x ^{2}}{2} - \frac{7 e x ^{2}}{2} + 14 e x + C

Solution steps

\int 3 x - 1 \cdot x - 7 e x + 14 e 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 3 x d x - \int 1 \cdot x d x - \int 7 e x d x + \int 14 e d x

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

\int 1 \cdot x d x = \frac{x ^{2}}{2}

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

\int 14 e d x = 14 e x

= \frac{3 x ^{2}}{2} - \frac{x ^{2}}{2} - \frac{7 e x ^{2}}{2} + 14 e x

Add a constant to the solution

= \frac{3 x ^{2}}{2} - \frac{x ^{2}}{2} - \frac{7 e x ^{2}}{2} + 14 e x + C

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

x \to 3 lim (2 x^{2} - 7 x + 6)

\frac{d}{d x} (\frac{n}{x + 1})

\int \frac{1}{x \cdot 1 - x} d x

\frac{1}{( x - 1 )}

What is the integral of (3x-1x-7ex+14e) ?
The integral of (3x-1x-7ex+14e) is (3x^2)/2-(x^2)/2-(7ex^2)/2+14ex+C