_ ^ dx x( x^5 + 1) = - Vidyadip

MCQ

$\int_{}^{} {\frac{{dx}}{{x({x^5} + 1)}}} = $

A
$\frac{1}{5}\log {x^5}({x^5} + 1) + c$
B
$\frac{1}{5}\log {x^5}\left( {\frac{{1 + {x^5}}}{{{x^5}}}} \right) + c$
C
$\frac{1}{5}\log {x^5}\left( {\frac{{{x^5}}}{{{x^5} + 1}}} \right) + c$
✓
None of these

✓

Answer

Correct option: D.

None of these

d
(d) We have $I = \int {\frac{{dx}}{{x({x^5} + 1)}}} = \int {\frac{{dx}}{{{x^6}\left( {1 + \frac{1}{{{x^5}}}} \right)}}} $
Put $1 + \frac{1}{{{x^5}}} = t$ ==> $\frac{{ - 5}}{{{x^6}}}dx = dt$
==> $I = - \frac{1}{5}\int {\frac{{dt}}{t} = - \frac{1}{5}} \log t + c$
$I = - \frac{1}{5}\log \left( {1 + \frac{1}{{{x^5}}}} \right) + c = - \frac{1}{5}\log \left( {\frac{{{x^5} + 1}}{{{x^5}}}} \right) + c$
$I = \frac{1}{5}\log \left( {\frac{{{x^5}}}{{{x^5} + 1}}} \right) + c$.

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 7.1 inderfinite integral→7.1 inderfinite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

In a study about a pandemic, data of $900$ persons was collected. It was found that

$190$ persons had symptom of fever,

$220$ persons had symptom of cough,

$220$ persons had symptom of breathing problem,

$330$ persons had symptom of fever or cough or both,

$350$ persons had symptom of cough or breathing problem or both,

$340$ persons had symptom of fever or breathing problem or both,

$30$ persons had all three symptoms (fever, cough and breathing problem).

If a person is chosen randomly from these 900 persons, then the probability that the person has at most one symptom is. . . . .

The radius of a cylinder is increasing at the rate of $3\,\,m/sec$ and its altitude is decreasing at the rate of $4 \,m/sec$. The rate of change of volume when radius is $ 4 $ metres and altitude is $6 $ metres is

If ${e^y} + xy = e$, the ordered pair $\left( {\frac{{dy}}{{dx}},\frac{{{d^2}y}}{{d{x^2}}}} \right)$ at $x = 0$ is equal to

The value of $\int\frac{\sin\text{x}+\cos\text{x}}{\sqrt{1-\sin2\text{x}}}\text{ dx}$ is equal to:

$\sqrt{\sin2\text{x}}+\text{C}$
$\sqrt{\cos2\text{x}}+\text{C}$
$\pm(\sin\text{x}-\cos\text{x})+\text{C}$
$\pm\log(\sin\text{x}-\cos\text{x})+\text{C}$

Find the values of $a, b, c$ and $d$ respectively if $\left[\begin{array}{cc}2 a+b & a-2 b \\ 5 c-d & 4 c+3 d\end{array}\right]=\left[\begin{array}{cc}4 & -3 \\ 11 & 24\end{array}\right]$.

The maximum number of equivalence relations on the set A = {1, 2, 3} is:

1
2
3
5

If a random variable $X$ follows the Binomial distribution $B (33, p )$ such that $3 P ( X =0)= P ( X =1)$, then the value of $\frac{ P ( X =15)}{ P ( X =18)}-\frac{ P ( X =16)}{ P ( X =17)}$ is equal to

Linear programming model which involves funds allocation of limited investment is classified as:

Ordination budgeting model
Capital budgeting models
Funds investment models
Funds origin models

Let $h(x) = \min \{ x,\,{x^2}\} ,$ for every real number of $x$. Then

The point which does not lie in the half - plane 2x + 3y -12 < 0 is: