Question

pls help with full process
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Answer 1

Answer:

The integral is $8Sin^{-1}x + 5\sqrt{1-x^{2} }$

Step-by-step explanation:

$\int {\frac{5x+8}{\sqrt{1-x^{2} } } } \, dx$

The above integration will be solved by uv integration method.

$\int{uv} \, dx$

$u\int{v} \, dx - \int{u^{'}\int{v} \, dx } \, dx$

let u= 5x + 8  , v= 1/$\sqrt{1-x^{2} }$

$\int {\frac{5x+8}{\sqrt{1-x^{2} } } } \, dx$

$5x+8\int{1/\sqrt{1-x^{2} } } \, dx - \int{\frac{d(5x+8)}{dx} \int{1/\sqrt{1-x^{2} }} \, dx } \,\ dx$

(5x+8)$Sin^{-1}x$ - $\int{5* sin^{-1} } \, dx$

(5$x$+8)$Sin^{-1}x$- 5($xSin^{-1} x - \sqrt{1-x^{2} }$)

5$x$$Sin^{-1}x$ +8$Sin^{-1}x$ - 5$x$$Sin^{-1}x$ + $\sqrt{1-x^{2} }$

8$Sin^{-1}x$ + $\sqrt{1-x^{2} }$