What is the integral of 5x+sqrt(x) ?

The integral of 5x+sqrt(x) is (5x^2)/2+2/3 x^{3/2}+C

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integral of 5x+sqrt(x)

\int 5 x + x d x

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

Solution steps

\int 5 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 5 x d x + \int x d x

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

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

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

Add a constant to the solution

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

\frac{x ( x + 1 ) d y}{d x} + x y = 1, y (e) = 1

y = \frac{4 x - 7 - x}{5}

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

\int_{0}^{1} x (x - x) d x

\frac{d}{d x} (ln (x - 2))

What is the integral of 5x+sqrt(x) ?
The integral of 5x+sqrt(x) is (5x^2)/2+2/3 x^{3/2}+C