The value of int frac{dx}{xsqrt{x^4 - 1}} is | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $I = \int \frac{dx}{x\sqrt{x^4 - 1}}$.Multiply the numerator and denominator by $x$:$I = \int \frac{x \, dx}{x^2 \sqrt{(x^2)^2 - 1}}$.Substitu

Vedclass · Accepted Answer

$\frac{1}{2} \sec^{-1}(x^2) + k$

Vedclass · Answer

(A) Let $I = \int \frac{dx}{x\sqrt{x^4 - 1}}$.Multiply the numerator and denominator by $x$:$I = \int \frac{x \, dx}{x^2 \sqrt{(x^2)^2 - 1}}$.Substitute $t = x^2$,then $dt = 2x \, dx$,which implies $x \, dx = \frac{dt}{2}$.Substituting these into the integral:$I = \int \frac{dt/2}{t \sqrt{t^2 - 1}} = \frac{1}{2} \int \frac{dt}{t \sqrt{t^2 - 1}}$.Using the standard integral formula $\int \frac{dt}{t \sqrt{t^2 - 1}} = \sec^{-1}(t) + k$:$I = \frac{1}{2} \sec^{-1}(t) + k$.Substituting back $t = x^2$:$I = \frac{1}{2} \sec^{-1}(x^2) + k$.

The value of $\int \frac{dx}{x\sqrt{x^4 - 1}}$ is

Similar Questions

If $\int \frac{e^x-1}{e^x+1} dx = f(x) + c$, then $f(x)$ is equal to

The value of $\lambda$ for which $\int \frac{4x^3 + \lambda 4^x}{4^x + x^4} \, dx = \log (4^x + x^4) + c$ is

Let $f(x) = \frac{1}{x} \ln \left( \frac{x}{e^x} \right)$,then its primitive with respect to $x$ is:

Write an anti-derivative for the following function using the method of inspection: $\frac{1}{x}, x \neq 0$

$\int \frac{dx}{\sqrt{x + a} + \sqrt{x + b}} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module