Question

2x³+18x-1/x²+9,Integrate the given function w.r.t. x considering them well defined and integrable over proper domain.

Answer 1

we have to integrate (2x³ + 18x - 1)/(x² + 9)

rearrange (2x³ + 18x - 1) in such a way that it contains (x² + 9)
e.g., 2x³ + 18x - 1 = 2x(x² + 9) - 1

$\int{\frac{2x(x^2+9)-1}{x^2+9}}\,dx$

$=\int{\frac{2x(x^2+9)}{x^2+9}}\,dx-\int{\frac{1}{x^2+9}}\,dx$

$=\int{2x}\,dx-\int{\frac{1}{x^2+3^2}}\,dx$

$=2\frac{x^2}{2}-\frac{1}{3}tan^{-1}\frac{x}{3}+C$

$=x^2-\frac{1}{3}tan^{-1}\frac{x}{3}+C$

Answer 2

Answer:

Step-by-step explanation:

10+10