Download App

STD 12 - 7.1 inderfinite integral — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {\frac{{5({x^6} + 1)}}{{{x^2} + 1}}dx = } $
  • A
    $5({x^7} + x){\tan ^{ - 1}}x + c$
  • ✓
    ${x^5} - \frac{5}{3}{x^3} + 5x + c$
  • C
    $3{x^4} - 5{x^2} + 15x + c$
  • D
    $5{\tan ^{ - 1}}({x^2} + 1) + \log ({x^2} + 1) + c$
✓

Answer

Correct option: B.
${x^5} - \frac{5}{3}{x^3} + 5x + c$
b
(b)$\int_{}^{} {\frac{{5({x^6} + 1)}}{{{x^2} + 1}}\,dx = \int_{}^{} {\frac{{5({x^2} + 1)({x^4} - {x^2} + 1)}}{{({x^2} + 1)}}\,dx} } $
$ = \int_{}^{} {5({x^4} - {x^2} + 1)\,dx = {x^5} - \frac{5}{3}{x^3} + 5x + 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

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 7.1 inderfinite integral→STD 12 - 7.1 inderfinite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Consider a function $f : N \rightarrow R$, satisfying $f(1)+2 f(2)+3 f(3)+\ldots+x f(x)=x(x+1) f(x) ; x \geq 2$ with $f(1)=1$. Then $\frac{1}{f(2022)}+\frac{1}{f(2028)}$ is equal to
→
$\int_{}^{} {{x^5}.{e^{{x^2}}}dx = } $
→
The objective function of an LPP is
→
If the sum of the matrices $\begin{bmatrix}\text{x}\\\text{x}\\\text{y}\end{bmatrix},\begin{bmatrix}\text{x}\\\text{y}\\\text{z}\end{bmatrix}$ and $\begin{bmatrix}\text{z}\\0\\0\end{bmatrix}$ is the matrix $\begin{bmatrix}10\\5\\5\end{bmatrix},$ then what is the value of y ?
→
The value of $\int_{ - 1}^1 {\frac{{\sin x - {x^2}}}{{3 - |x|}}\,dx} $ is
→
If the distance  $‘s’$  traveled by a particle in time $ t$ is $s = a\sin t + b\cos 2t$, then the acceleration at $ t = 0$ is
→
If $A$ and $B$ are two events such that $P\,(A) \ne 0$ and $P\,(B) \ne 1,$ then $P\left( {\frac{{\overline A }}{{\overline B }}} \right) = $
→
Evaluate: $\int\left(e^{x \log a}+e^{a \log x}+e^{a \log a}\right) d x$
→
Let $\mathrm{A}(-1,1)$ and $\mathrm{B}(2,3)$ be two points and $\mathrm{P}$ be a variable point above the line $A B$ such that the area of $\triangle \mathrm{PAB}$ is $10$ . If the locus of $\mathrm{P}$ is $\mathrm{ax}+\mathrm{by}=15$, then $5 a+2 b$ is :
→
Let $f:[0, \infty) \rightarrow[0,3]$ be a function defined by

$f(x)=\max \{\sin t: 0 \leq t \leq x\}, \quad 0 \leq x \leq \pi$

$\quad \quad \quad \quad \quad \quad 2+\cos x,\quad \quad \quad \quad x>\pi$

Then which of the following is true?

→