Evaluate 1 x(1+ ) dx - Vidyadip

Question

Evaluate $\int\frac{1}{\text{x}(1+\log\text{x})}\text{ dx}$

✓

Answer

$\text{I}=\int\frac{1}{\text{x}(1+\log\text{x})}\text{ dx}$
Let $(1+\log\text{x})=\text{t}$
Or, $\frac{1}{\text{x}}\text{dx}=\text{dt}$
$\text{I}=\int\frac{1}{\text{t}}\text{dt}$
$\text{I}=\log|\text{t}|+\text{C}$
$\therefore\ \text{I}=\log|1+\log\text{x}|+\text{C}$

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 "3 Marks" from INTEGRALS→INTEGRALS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Show that the points $A\left( {2\hat i - \hat j + \hat k} \right),B\left( {\hat i - 3\hat j - 5\hat k} \right),C\left( {3\hat i - 4\hat j - 4\hat k} \right)$ are the vertices of a right angled triangle.

Show that $\text{AB}\neq\text{BA}$ in the following cases:
$\text{A}=\begin{bmatrix}-1&1&0\\0&-1&1\\2&3&4\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&2&3\\0&1&0\\1&1&0\end{bmatrix}$

Write the position vector of the point which divdes the join of the points with position vectors $3\vec{\text{a}} - 2\vec{\text{b}} $ and $2\vec{\text{a}} + 3\vec{\text{b}} $ in the ratio 2 : 1.

Find the equation of the plane passing through (a, b, c) and parallel to the plane $\vec{\text{r}}\cdot(\text{i}+\hat{\text{j}}+\hat{\text{k}})=2$

If a function g = {(1, 1), (2, 3), (3, 5), (4, 7)} is described by $\text{g(x)}=\alpha\text{x}+\beta\alpha\text{x}+\beta,$ then find the values of $\alpha$ and $\beta.$

$\begin{array}{l}\text { Find } \frac{d^2 y}{d x^2}: \\ x=a\left(\cos t+\log \tan \frac{t}{2}\right), y=a \sin t\end{array}$

Find gof and fog when f : R → R and g : R → R are defined by:
f(x) = 8x³ and $\text{g(x)}=\text{x}^\frac{1}{3}$

Evaluate the following integrals:
$\int^\limits4_1\text{f(x)}\text{dx},$ Where $\text{f(x)}=\begin{cases}4\text{x}+3,&\text{if }\ 1\leq\text{x}\leq2\\3\text{x}+5,&\text{if }\ 2\leq\text{x}\leq4\end{cases}$

Evaluate the following integrals:
$\int\frac{1}{\text{x}\sqrt{\text{x}^4-1}}\text{ dx}$

Find the angle between the line $\frac{\text{x}+1}{2}=\frac{\text{y}}{3}=\frac{\text{z}-3}{6}$ and the plane 10x + 2y - 11z = 3.