What is the integral of (5x^2-15x+45/4)^{1/2} ?

The integral of (5x^2-15x+45/4)^{1/2} is (5^{1/2})/2 (x^2-3x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (5x^2-15x+45/4)^{1/2}

\int (5 x^{2} - 15 x + \frac{45}{4})^{\frac{1}{2}} d x

\frac{5 ^{\frac{1}{2}}}{2} (x^{2} - 3 x) + C

Solution steps

\int (5 x^{2} - 15 x + \frac{45}{4})^{\frac{1}{2}} d x

Simplify

(5 x^{2} - 15 x + \frac{45}{4})^{\frac{1}{2}} : \frac{5 ^{\frac{1}{2}}}{2} (2 x - 3)

= \int \frac{5 ^{\frac{1}{2}}}{2} (2 x - 3) d x

Take the constant out:

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

= \frac{5 ^{\frac{1}{2}}}{2} \cdot \int 2 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

= \frac{5 ^{\frac{1}{2}}}{2} (\int 2 x d x - \int 3 d x)

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

\int 3 d x = 3 x

= \frac{5 ^{\frac{1}{2}}}{2} (x^{2} - 3 x)

Add a constant to the solution

= \frac{5 ^{\frac{1}{2}}}{2} (x^{2} - 3 x) + C

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

\int \frac{6}{1 + 3 x} d x

\int - \frac{20 arctan ( 2 x )}{1 + 4 x ^{2}} d x

\int (5 x^{2} + 7 x + \frac{1}{x ^{3}}) d x

\int x^{9} ln (3 x^{5}) d x

What is the integral of (5x^2-15x+45/4)^{1/2} ?
The integral of (5x^2-15x+45/4)^{1/2} is (5^{1/2})/2 (x^2-3x)+C