int {frac{{a{x^3} + b{x^2} + c}}{{{x^4}}},dx} | vedclass

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

Question

(C) Given integral: $I = \int {\frac{{a{x^3} + b{x^2} + c}}{{{x^4}}}dx}$ Divide each term in the numerator by the denominator: $I = \int {\left( {\fra

Vedclass · Accepted Answer

$a\log |x| - \frac{b}{x} - \frac{c}{3{x^3}} + C$

Vedclass · Answer

(C) Given integral: $I = \int {\frac{{a{x^3} + b{x^2} + c}}{{{x^4}}}dx}$ Divide each term in the numerator by the denominator: $I = \int {\left( {\frac{{a{x^3}}}{{{x^4}}} + \frac{{b{x^2}}}{{{x^4}}} + \frac{c}{{{x^4}}}} \right)dx}$ $I = \int {\left( {\frac{a}{x} + \frac{b}{{{x^2}}} + \frac{c}{{{x^4}}}} \right)dx}$ $I = \int {\frac{a}{x}dx + \int {b{x^{ - 2}}dx + \int {c{x^{ - 4}}dx} } }$ Using the integration formulas $\int {\frac{1}{x}dx = \log |x|}$ and $\int {{x^n}dx = \frac{{{x^{n + 1}}}}{{n + 1}}}$: $I = a\log |x| + b\left( {\frac{{{x^{ - 1}}}}{{ - 1}}} \right) + c\left( {\frac{{{x^{ - 3}}}}{{ - 3}}} \right) + C$ $I = a\log |x| - \frac{b}{x} - \frac{c}{{3{x^3}}} + C$ Thus,the correct option is $C$.

$\int {\frac{{a{x^3} + b{x^2} + c}}{{{x^4}}}\,dx} $ equals to

Similar Questions

If $\int \frac{dx}{32-2x^2} = A \log(4-x) + B \log(4+x) + c$,then the values of $A$ and $B$ are respectively (where $c$ is a constant of integration).

$\int {\frac{{3{x^3} - 2\sqrt x }}{x}} dx = $

Find the following integral: $\int \sqrt{x}(3x^{2} + 2x + 3) dx$

$\int \sqrt{1+x^{2}} \, dx$ is equal to

For $-\frac{\pi}{2} < x < \frac{\pi}{2}$,evaluate the integral $\int \tan^{-1} \left( \sqrt{\frac{1 - \sin x}{1 + \sin x}} \right) dx$ (where $C$ is a constant of integration).

Vedclass Test Series

Exam Paper Generator

Online Exam Module