Question

Answer the above THE BEST WILL GET BRAINLIEST
Note: if you randomly wrote anything you will be reported
PS: You will not get the answer in google so don't waste your time!!​

Answer 1

Answer:

$\frac{-cos(5-7x)}{7} +c$

Step-by-step explanation:

Hey there, Math Lovers.

you can directly use the formula that:

if, $\int {g(x)} \, dx$ = F(x) + C       (where c is an arbitrary constant)

then, $\int {g(ax+b)} \, dx = \frac{F(ax+b)}{a} + C$.

now, $\int {sinx} \, dx = cosx + C$$\int{sinx} \, dx= cosx + C$

THUS, $\int {sin(5-7x)} \, dx = \frac{-cos(5-7x)}{7} + C.$

For the Proof By Substitution , Read Below.

Let  $\int {g(x)} \, dx$ = F(x) + C  for some function g(x).

Now , Consider  $\int{g(ax+b)} \, dx$

let u = ax+b  ⇒    $\frac{du}{dx}=a$  ⇒  dx = (du/a).

so,  $\int{g(ax+b)} \, dx$ = $\int {g(u)} \, \frac{du}{a}$  --------------------------(put ax+b = u and dx = (du/a)

⇒   $\int{g(ax+b)} \, dx$  =  $\frac{1}{a}\int {g(u)} \, du$ = $\frac{1}{a}\int {g(ax+b)} \, d(ax+b)$ ------------(put u = ax+b)

⇒   $\int {g(ax+b)} \, dx = \frac{F(ax+b)}{a} + C$.

hence, proved.

Now, please mark me as the brainliest.