If int frac{dx}{x + x^7} = p(x),then int frac | vedclass

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

Question

(A) We are given that $\int \frac{dx}{x + x^7} = p(x)$.Consider the integral $I = \int \frac{x^6}{x + x^7} dx$.We can rewrite the integrand as:$I = \i

Vedclass · Accepted Answer

$\ln |x| - p(x) + c$

Vedclass · Answer

(A) We are given that $\int \frac{dx}{x + x^7} = p(x)$.Consider the integral $I = \int \frac{x^6}{x + x^7} dx$.We can rewrite the integrand as:$I = \int \frac{x^6}{x(1 + x^6)} dx = \int \frac{x^5}{1 + x^6} dx$.Alternatively,we can manipulate the original expression:$I = \int \frac{x^6}{x(1 + x^6)} dx = \int \frac{(1 + x^6) - 1}{x(1 + x^6)} dx$.Splitting the integral,we get:$I = \int \frac{1 + x^6}{x(1 + x^6)} dx - \int \frac{1}{x(1 + x^6)} dx$.$I = \int \frac{1}{x} dx - \int \frac{1}{x + x^7} dx$.Since $\int \frac{1}{x} dx = \ln |x| + c_1$ and $\int \frac{1}{x + x^7} dx = p(x) + c_2$,we have:$I = \ln |x| - p(x) + c$.

If $\int \frac{dx}{x + x^7} = p(x)$,then $\int \frac{x^6}{x + x^7} dx$ is equal to

Similar Questions

$\int \frac{1}{[{(x - 1)}^3 {(x + 2)}^5]^{1/4}} \,dx$ is equal to

$\int \frac{dx}{(1+x) \sqrt{8+7x-x^2}} = $

If the value of the integral $\int_{1}^{2} e^{x^2} dx$ is $\alpha$,then the value of $\int_{e}^{e^4} \sqrt{\ln x} dx$ is:

$\begin{aligned} & \text{If } 5(f(x))^2 = x f(x) + 30 \text{ and } \\ & \int \frac{3 x^3 + (1 - 30 x^2) f(x)}{(10 f(x) - x)(x^3 - f(x))^2} dx \\ & = \frac{A}{B x^3 + D f(x)} + C, \text{ then } A + B + D = \end{aligned}$

$\int \sqrt{x^{2}-8 x+7} \, dx$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module