What is the integral of 7x-sqrt(x) ?

The integral of 7x-sqrt(x) is (7x^2)/2-2/3 x^{3/2}+C

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integral of 7x-sqrt(x)

\int 7 x - x d x

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

Solution steps

\int 7 x - x 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 d x - \int x d x

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

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

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

Add a constant to the solution

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

y = ln (- 3 x^{6})

(1 + y^{2}) d x - (x^{2} + 1) d y = 0

\frac{\partial}{\partial x} (\frac{- y ^{4}}{4 x ^{4}})

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

f (x) = 2 x^{2} + 2 x, (- 2, - 6)

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