What is the integral of 45(1+sqrt(x)) ?

The integral of 45(1+sqrt(x)) is 45(x+2/3 x^{3/2})+C

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integral of 45(1+sqrt(x))

\int 45 (1 + x) d x

45 (x + \frac{2}{3} x^{\frac{3}{2}}) + C

Solution steps

\int 45 (1 + x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 45 \cdot \int 1 + 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

= 45 (\int 1 d x + \int x d x)

\int 1 d x = x

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

= 45 (x + \frac{2}{3} x^{\frac{3}{2}})

Add a constant to the solution

= 45 (x + \frac{2}{3} x^{\frac{3}{2}}) + C

\frac{\partial}{\partial x} (ln (x^{y}))

x \to 0 lim (\frac{1}{x} - \frac{1}{e ^{t} - 1})

x \to 4 lim (\frac{3 x + 4}{x - 2})

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

\frac{d}{d x} (\frac{a}{x ^{3}})

What is the integral of 45(1+sqrt(x)) ?
The integral of 45(1+sqrt(x)) is 45(x+2/3 x^{3/2})+C