Evaluate the following integrals: (2+3 ) x dx - Vidyadip

Question

Evaluate the following integrals:
$\int\frac{\sin(2+3\log\text{x})}{\text{x}}\text{ dx}$

✓

Answer

$\int\frac{\sin(2+3\log\text{x})}{\text{x}}\text{ dx}$ Let $2+3\log\text{x}=\text{t}$ $\Rightarrow\frac{3}{\text{x}}=\frac{\text{dt}}{\text{dx}}$ $\Rightarrow\frac{\text{dx}}{\text{x}}=\frac{\text{dt}}{3}$ Now, $\int\frac{\sin(2+3\log\text{x})}{\text{x}}\text{ dx}$$=\frac{1}{3}\int\sin\text{t dt}$
$=\frac{1}{3}[-\cos\text{t}]+\text{C}$
$=-\frac{1}{3}\cos(2+3\log\text{x})+\text{C}$

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 Question" 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

Find the points o local maxima or local minima, if any, of the following functions, using the first derivatives test. Also, find the local maximum or local minimum values, as the case may be:
$\text{f}'(\text{x})=\text{x}^{3}(2\text{x}-1)^{3}$

Let $\text{A}=\begin{bmatrix}2&-3\\-7&5\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&0\\2&-4\end{bmatrix},$ verify that
$(\text{A}+\text{B})^\text{T}=\text{A}^\text{T}+\text{B}^\text{T}$

If a machine is correctly set up it produces $90 \%$ acceptable items. If it is incorrectly set up it produces only $40 \%$ acceptable item. Past experience shows that $80 \%$ of the setups are correctly done. If after a certain set up, the machine produces $2$ acceptable items, find the probability that the machine is correctly set up.

Are the following set of ordered pairs functions? If so, examine whether the mapping is injective or surjective.

{(x, y): x is a person, y is the mother of x}.
{(a, b): a is a person, b is an ancestor of a}.

Differentiate the following functions with respect to x:
$\tan^{-1}\Big(\frac{\sin\text{x}}{1+\cos\text{x}}\Big),\pi<\text{x}<\pi$

Using determinants, find the equation of the line joining the points:
$(3, 1)$ and $(9, 3)$

Define a symmetric matrix. Prove that for $\text{A}=\begin{bmatrix}2&4 \\5&6 \end{bmatrix},$ $A + A^T$ is a symmetric matrix where $A^T$ is the transpose of $A$.

Find the values of 'a' for which hte function $\text{f}(\text{x})=\sin\text{x}-\text{a}\text{x}+4$ is increasing function on R.

Evaluate the following integrals:$\int\frac{1}{\sqrt{8+3\text{x}-\text{x}^2}}\text{ dx}$

For the binary operation $\times _7$ on the set $S = \{1, 2, 3, 4, 5, 6\},$ compute $3^{−1} \times _7 4.$