Question

Integration of dx/3x+5=?
Step by step solution please..and please don't spam

Answer 1

Mistake in question :

Correct question :

Integrate ( 3 x + 5 ) d x .

Answer:

$\large \int {(3x+5)}=\dfrac{3}{2}.x^{2}+5x+c$

Explanation:

Given :

y = 3 x + 5

We have to integrate y with respect to x.

Applying power rule here

$\large \text{ \int {x^n} \, dx=\dfrac{x^{n+1}}{n+1}+c }$

Now

$\large \int {(3x+5)}=\int{3x} \, dx+ \int{5} \, dx +c\\\\\\\large \text{ \int {(3x+5)}=\dfrac{3x^{1+1}}{1+1}+\dfrac{5x^{0+1}}{0+1}+c }\\\\\\\large \text{ \int {(3x+5)}=\dfrac{3x^{2}}{2}+\dfrac{5x^{1}}{1}+c }\\\\\\\large \int {(3x+5)}=\dfrac{3}{2}x^{2}+5x+c$

Thus we get answer.

Answer 2

Explanation:

integrate (3x+5)dx =

$=\int (3x)dx + \int (5)dx$

$= 3\int (x) dx + \int (5)dx$

integration wrt x

$= 3 \times \frac{ x^{(1+1)}}{(1+1) }+ 5x +c$

$=( \frac{3x^2} { 2 }) + 5x + c$

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

therefor,

$\int (3x + 5 )dx =\\ \frac{3}{2} x^2 + 5x + c$

integration rules used for the given question :-

$\int x^n = \frac{x^{n+1}}{(n+1)}+c$

$\int kdx = kx + c$