Question
Evaluate the following integrals:
$\int\frac{1}{(\text{x}+1)(\text{x}^2+2\text{x}+2)}\text{ dx}$
$\int\frac{1}{(\text{x}+1)(\text{x}^2+2\text{x}+2)}\text{ dx}$
Let
$\text{x}+1=\tan\text{u}$ $\Rightarrow\text{dx}=\sec^2\text{u du}$ $\therefore\ \text{I}=\int\frac{\sec^2\text{u}}{\tan\text{u}(\tan^2\text{u}+1)}\text{ du}$ $=\int\frac{\cos\text{u}}{\sin\text{u}}\text{ du}$ $=\log|\sin\text{u}|+\text{C}$ $=\log\Big|\frac{\tan\text{u}}{\sec^2\text{u}}\Big|+\text{C}$ $=\log\bigg|\frac{\text{x}+1}{\sqrt{\text{x}^2+2\text{x}+2}}\bigg|+\text{C}$Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$\int\sin^{-1}(3\text{x}-4\text{x}^3)\text{dx}$
$\int\frac{\text{x}\cos^{-1}\text{x}}{\sqrt{1-\text{x}^3}}\text{dx}$
A(-6, 3), B(-2, -5)
Find $\Big|\overrightarrow{\text{AB}}\Big|$
| X = xi | 0 | 1 | 2 | 3 |
| P(X = xi) | 2k4 | 3k2 - 5k3 | 2k - 3k2 | 3k - 1 |
$\int\text{x}\sin\text{x}\cos\text{x dx}$