Question
Integrate the following functions w.r.t. x:
$x^2\left(1-\frac{2}{x}\right)^2$
$x^2\left(1-\frac{2}{x}\right)^2$
✓
Answer
$\quad \int x^2\left(1-\frac{2}{x}\right)^2 d x=\int x^2\left(1-\frac{4}{x}+\frac{4}{x^2}\right) d x$
$=\int\left(x^2-4 x+4\right) d x$
$=\int x^2 d x-4 \int x d x+4 \int 1 d x$
$=\frac{x^3}{3}-4\left(\frac{x^2}{2}\right)+4 x+c$
$=\frac{1}{3} x^3-2 x^2+4 x+c$
$=\int\left(x^2-4 x+4\right) d x$
$=\int x^2 d x-4 \int x d x+4 \int 1 d x$
$=\frac{x^3}{3}-4\left(\frac{x^2}{2}\right)+4 x+c$
$=\frac{1}{3} x^3-2 x^2+4 x+c$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If $A=\left[\begin{array}{lll}1 & 2 & 3 \\ 1 & 1 & 5 \\ 2 & 4 & 7\end{array}\right]$, then find the value of $a_{31} A_{31}+a_{32} A_{32}+a_{33} A_{33}$
→Evaluate :
→$\int_{-3}^3 \frac{x^3}{9-x^2} \cdot d x$
If $A=\left[\begin{array}{ccc}2 & -1 & 1 \\ -2 & 3 & -2 \\ -4 & 4 & -3\end{array}\right]$ the find $A^2$
→Construct a 4 × 3 matrix whose element are:
$\text{a}_\text{ij}=\frac{\text{i}-\text{j}}{\text{i}+\text{j}}$
→$\text{a}_\text{ij}=\frac{\text{i}-\text{j}}{\text{i}+\text{j}}$
Find a unit vector in the opposite direction of $\overline{ u }$. Where $\overline{ u }=8 \hat{ i }+3 \hat{ j }-\widehat{ k }$
→Find $|\bar{u} \times \bar{v}|$ if
i)
→i)
Find the area enclosed between $y=\cos x$ and $X$-axis between the lines $x =\frac{\pi}{2}$ and $x \leq \frac{3 \pi}{2}$
→In each of the following examples verify that the given expression is a solution of the corresponding differential equation.
→$y = e ^{a x _x} ; x \frac{d y}{d x}= y \log y$
Evaluate: $\int \frac{1}{x^2+25} d x$
→$\int \frac{x}{x+2} d x$
→