Write a value of 1 x( )^ n dx - Vidyadip

Question

Write a value of $\int\frac{1}{\text{x}(\log\text{x})^{\text{n}}}\text{ dx}$

✓

Answer

Let $\text{I}=\int\frac{1}{\text{x}(\log\text{x})^{\text{n}}}\text{ dx}$
Let $\log\text{x}=\text{t}$
$\frac{1}{\text{x}}\text{ dx}=\text{dt}$
$\text{dx}=\text{xdt}$
$\therefore\ \text{I}=\int\frac{1}{\text{t}^{\text{n}}}\text{ dt}$
$=\frac{\text{t}^{-\text{n}+1}}{-\text{n}+1}+\text{C}$
$\text{I}=\frac{(\log\text{x})^{1-\text{n}}}{1-\text{n}}+\text{C}$

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

Write a value of $\int\frac{(\log\text{x})^{\text{n}}}{\text{x}}\text{ dx}$

Differentiate the following functions with respect to x:
$10^{(10^\text{x})}$

Evaluate $\begin{vmatrix}2&3&7\\13&17&5\\15&20&12\end{vmatrix}^2$

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

Show that the following point are coplanar:
(0, 4, 3), (-1, -5, -3), (-2, -2, 1) and (1, 1, -1)

Differentiate the functions given in Exercise:
$(\log\text{x})^{\cos\text{x}}$

Differentiate w.r.t. x the function in x^x + x^a + a^x + a^a , for some fixed a > 0 and x > 0.

Find $\frac{\text{dy}}{\text{dx}}$ when x and y are connected by the relation:
$\sec(\text{x}+\text{y})=\text{xy}$

Find the equation of the plane passing through the origin and perpendicular to each of the planes x + 2y - z = 1 and 3x - 4y + z = 5.

Evaluate the following intregals:
$\int\frac{\text{x}}{\sqrt{\text{x}^2+\text{x}+1}}\text{dx}$