Question

Select the basic integration formula you can use to find the indefinite integral.

Answer 1

Answer:

$\int \dfrac{du}{u}=\log|u|+C$

$\int u^n du=\dfrac{u^{n+1}}{n+1}+C$

$\int \dfrac{du}{u\sqrt{u^2-a^2}}=\dfrac{1}{a}\csc^{-1}(\dfrac{x}{a})+C$

Step-by-step explanation:

a.

$\int \dfrac{du}{u}=\log|u|+C$    $[\because \int \dfrac{dx}{x}=\log |x|+C]$

b.

$\int u^n du=\dfrac{u^{n+1}}{n+1}+C$    $[\because \int x^n dx=\dfrac{x^{n+1}}{n+1}+C]$

c.

$\int \dfrac{du}{u\sqrt{u^2-a^2}}=\dfrac{1}{a}\csc^{-1}(\dfrac{x}{a})+C$        $[\because \dfrac{adx}{x\sqrt{x^2-a^2}}=\csc^{-1}(\dfrac{x}{a})+C]$