MCQ
$\int_{}^{} {\frac{{{{({{\tan }^{ - 1}}x)}^3}}}{{1 + {x^2}}}\,dx = } $
  • A
    ${({\tan ^{ - 1}}x)^4} + c$
  • $\frac{{{{({{\tan }^{ - 1}}x)}^4}}}{4} + c$
  • C
    $2{\tan ^{ - 1}}x + c$
  • D
    $2{({\tan ^{ - 1}}x)^2} + c$

Answer

Correct option: B.
$\frac{{{{({{\tan }^{ - 1}}x)}^4}}}{4} + c$
b
(b) Put ${\tan ^{ - 1}}x = t \Rightarrow \frac{1}{{1 + {x^2}}}dx = dt$
 $\int_{}^{} {\frac{{{{({{\tan }^{ - 1}}x)}^3}}}{{1 + {x^2}}}} d\alpha = \int_{}^{} {{t^3}} dt = \frac{{{t^4}}}{4} + c$ = $\frac{{{{({{\tan }^{ - 1}}x)}^4}}}{4} + c$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

If $\alpha=\tan^{-1}\Big(\frac{\sqrt3\text{x}}{2\text{y}-\text{x}}\Big),\beta=\tan^{-1}\Big(\frac{2\text{x}-\text{y}}{\sqrt3\text{y}}\Big),$ then $\alpha-\beta=$
Let the vectors $\overline{\mathrm{PQ}}, \overline{\mathrm{QR}}, \overline{\mathrm{RS}}, \overline{\mathrm{ST}}, \overline{\mathrm{TU}}$ and $\overline{\mathrm{UP}}$ represent the sides of a regular hexagon.

$STATEMENT$ $-1: \overline{\mathrm{PQ}} \times(\overline{\mathrm{RS}}+\overline{\mathrm{ST}}) \neq \overrightarrow{0}$. because

$STATEMENT$ $-2: \overline{\mathrm{PQ}} \times \overline{\mathrm{RS}}=\overrightarrow{0}$ and $\overline{\mathrm{PQ}} \times \overline{\mathrm{ST}} \neq \overrightarrow{0}$.

The constant value ($\lambda$  + $\mu$) for which the lines $\vec{r}$ = $2\hat{i}$ + $\hat{j}$ + $\hat{k}$ + $\lambda$($\hat{i} - 2\hat{j}$) and $\vec{r}$ = $\hat{i}$ + $\hat{j}$ - $3\hat{k}$ + $\mu$ ($\hat{j} + 2\hat{k}$) intersect each other, is equal to (where $\lambda$ & $\mu$ are parameters)
$\int_{}^{} {{e^x}[\tan x - \log (\cos x)]\;dx = } $
The area of region bounded by $y= \sin x $ and $x-$ axis is, when $0 \leq x \leq 2n \ ($in sq units$)$
If the vectors $3 \hat{i}+2 \hat{j}-\hat{k}$ and $6 \hat{i}-4 p \hat{j}+q \hat{k}$ are parallel. Then the values of $p$ and $q$ will respectively be :
The number of functions defined from $\{1,2,3,4,5\} \rightarrow\{a, b\}$ which are one-one is
Choose the correct option from given four options$:\ \int\text{e}^\text{x}\Big(\frac{1-\text{x}}{1+\text{x}^2}\Big)^2\text{dx}$ is equal to:
$\int_0^a {{x^2}\sin {x^3}\,dx} $ equals
If the determinant $\begin{vmatrix}\text{a}&\text{b}&2\text{a}\alpha+3\text{b}\\\text{b}&\text{c}&2\text{b}\alpha+3\text{c}\\2\text{a}\alpha+ 3\text{b}&2\text{b}\alpha+3\text{c}&0\end{vmatrix}=0,$ then :