Evaluate the following integrals: ( ) x dx - Vidyadip

Question

Evaluate the following integrals:
$\int\frac{\sin(\log\text{x})}{\text{x}}\text{ dx}$

✓

Answer

Let $\text{I}=\int\frac{\sin(\log\text{x})}{\text{x}}\text{ dx}\ ....(1)$ Let $\log\text{x}=\text{t}$ then, $\text{d}(\log\text{x})=\text{dt}$ $\Rightarrow\frac{1}{\text{x}}\text{ dx}=\text{dt}$ Putting $\log\text{x}=\text{t}$ and $\frac{1}{\text{x}}\text{ dx}=\text{dt}$ in equation (1), We get,$\text{I}=\int\sin\text{t dt}$
$=-\cos\text{t}+\text{C}$
$=-\cos\big(\log\text{x}\big)+\text{C}$

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 Question" from Indefinite Integrals→Indefinite Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Evaluate the definite integral in Exercise:$\int_{1}^{2}(4\text{x}^{3}-5\text{x}^{2}+6\text{x}+9)\text{dx}$

Find $\int \frac{x^2-3 x+1}{\sqrt{1-x^2}} d x$

On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

Construct the composition table for $\times _4$ on set $S = \{0, 1, 2, 3\}.$

Differentiate the function with respect to x : $\cos {x^3}{\sin ^2}\left( {{x^5}} \right)$

Find the mean and standard deviation of the following probability distributions:

$\text{x}_\text{i}$	$-5$	$-4$	$1$	$2$
$\text{p}_\text{i}$	$\frac{1}{4}$	$\frac{1}{8}$	$\frac{1}{2}$	$\frac{1}{8}$

If f(x) is an even function, then write whether f'(x) is even of odd.

Three relation $R_2$ is defined in set $A = \{a, b, c\}$ as follows:
$R_2 = \{(a, a)\}$
Find whether or not the relation $R_2$ on $A$ is:

Reflexive.
Symmetric.
Transitive.

Evaluate the integral in Exercise:
$\int\limits^{\frac{\pi}{2}}_{0}\sqrt{\sin\phi}\cos^{5}\phi\text{ d }\phi$

Consider the binary operation $*$ and o defined by the following tables on set $S = \{a, b, c, d\}.$

$o$	$a$	$b$	$c$	$d$
$a$	$a$	$a$	$a$	$a$
$b$	$a$	$b$	$c$	$d$
$c$	$a$	$c$	$d$	$b$
$d$	$a$	$d$	$b$	$c$