#### To determine

**To evaluate:**

The given integral.

#### Answer

-13ln5-3x+c

#### Explanation

**1) Concept:**

The substitution rule: If u=g(x) is a differentiable function whose range is I, and f is continuous on I, then ∫f(gx)g'xdx=∫f(u)du. Here g(x) is substituted as u and then differentiation

g’(x)dx =du

**2) Formula:**

i.

∫cf(x)dx=c∫f(x)dx

ii.

**∫1xdx=lnx+c**

**3) Given:**

∫dx5-3x

**4) Calculation:**

Consider the given integral ∫dx5-3x

Here using the substitution method

Substitute 5-3x=u,

Differentiating with respect to x

-3 dx=du

dx= -du3

Using this in given integral, it becomes,

∫dx5-3x

= ∫-du3u

By taking the constant terms outsidethe integral

= -13∫1u du

By usingtherules of integral

=-13lnu+c

Resubstituting u=5-3x in the above solution

= -13ln5-3x+c

**Conclusion:**

Therefore, ∫dx5-3x= -13ln5-3x+c