Question

How to integrate 1√x2−4x+3dx?

Answer 1

Answer: $- \frac{3x {}^{2} }{2} + 3x + C$

Step by step explanation :

$∫ \sqrt{x {}^{2} } - 4x + 3dx$

Any expression multiplied by 1 remains the same

$= > ∫ \sqrt{x {}^{2} } - 4x + 3dx$

Reduce the index of the radical and exponent with 2

$= > ∫x - 4x + 3 \: dx$

Collect the like terms by subtracting their coefficients

$= > ∫ - 3x + 3dx$

Use property of integral

$∫f(x) + - g(x)dx = ∫f(x)dx + - ∫g(x)dx$

$= > - ∫3xdx + ∫3dx$

Calculate the indefinite integral.

Use property of integral

$∫a \times f(x)dx = a \times ∫f(x)dx$

$= > - 3 \times ∫x \: dx + ∫3 \: dx$

Using $∫x \: dx = \frac{x {}^{2} }{2}$ , solve the integral.

$= > - 3 \times \frac{x {}^{2} }{2} + ∫3 \: dx$

Calculate the product

$= > - \frac{3x {}^{2} }{2} + ∫3 \: dx$

Using $∫ a \: dx = a \times x$, solve the integral

$= > - \frac{3x {}^{2} }{2} + 3x$

Add the constant of integration

$= > - \frac{3x {}^{2} }{2} + 3x + \: C$