English

CBSECommerce (English Medium) Class 12

Question Papers

Question Papers2489

Textbook Solutions20216

MCQ Online Mock Tests42

Important Solutions18873

Concept Notes & Videos242

∫ X 3 X − 2 D X - Mathematics

Advertisements

Advertisements

Question

\[\int\frac{x^3}{x - 2} dx\]

Sum

Solution

\[\int\left( \frac{x^3}{x - 2} \right)dx\]
\[ = \int\left( \frac{x^3 - 8 + 8}{x - 2} \right)dx\]
\[ = \int\left[ \frac{\left( x^3 - 2^3 \right)}{\left( x - 2 \right)} + \frac{8}{x - 2} \right]dx\]
\[ = \int\left[ \frac{\left( x - 2 \right)\left( x^2 + 2x + 4 \right)}{\left( x - 2 \right)} + \frac{8}{x - 2} \right]dx\]
\[ = \int\left( x^2 + 2x + 4 \right)dx + 8\int\frac{dx}{x - 2}\]
\[ = \frac{x^3}{3} + \frac{2 x^2}{2} + 4x + \text{8 ln} \left| x - 2 \right| + C\]
\[ = \frac{x^3}{3} + x^2 + 4x + \text{8 ln }\left| x - 2 \right| + C\]

shaalaa.com

Indefinite Integral Problems

Is there an error in this question or solution?

Chapter 19: Indefinite Integrals - Exercise 19.04 [Page 30]

APPEARS IN

RD Sharma Mathematics [English] Class 12

Chapter 19 Indefinite Integrals
Exercise 19.04 | Q 2 | Page 30

Video TutorialsVIEW ALL [1]

view
Video Tutorials For All Subjects
Indefinite Integral Problems

video tutorial00:39:37

RELATED QUESTIONS

\[\int\left( x^e + e^x + e^e \right) dx\]

\[\int\frac{\cos x}{1 - \cos x} \text{dx }or \int\frac{\cot x}{\text{cosec } {x }- \cot x} dx\]

\[\int \left( a \tan x + b \cot x \right)^2 dx\]

If f' (x) = 8x³ − 2x, f(2) = 8, find f(x)

\[\int\frac{1}{1 - \sin\frac{x}{2}} dx\]

\[\int\frac{1}{\sqrt{x + 3} - \sqrt{x + 2}} dx\]

\[\int\frac{2x + 1}{\sqrt{3x + 2}} dx\]

\[\int\frac{\cos 4x - \cos 2x}{\sin 4x - \sin 2x} dx\]

\[\int\frac{2 \cos 2x + \sec^2 x}{\sin 2x + \tan x - 5} dx\]

\[\int\frac{\sin 2x}{\left( a + b \cos 2x \right)^2} dx\]

` ∫ tan x sec^4 x dx `

` = ∫1/{sin^3 x cos^ 2x} dx`

\[\int\frac{\sec^2 x}{1 - \tan^2 x} dx\]

\[\int\frac{1}{x^{2/3} \sqrt{x^{2/3} - 4}} dx\]

\[\int\frac{\sin x - \cos x}{\sqrt{\sin 2x}} dx\]

\[\int\frac{x + 7}{3 x^2 + 25x + 28}\text{ dx}\]

\[\int\frac{1}{1 - \cot x} dx\]

\[\int\frac{1}{3 + 4 \cot x} dx\]

\[\int x \cos x\ dx\]

\[\int\frac{\text{ log }\left( x + 2 \right)}{\left( x + 2 \right)^2} \text{ dx }\]

\[\int \tan^{- 1} \left( \frac{2x}{1 - x^2} \right) \text{ dx }\]

\[\int \tan^{- 1} \sqrt{\frac{1 - x}{1 + x}} dx\]

\[\int\left( \frac{1}{\log x} - \frac{1}{\left( \log x \right)^2} \right) dx\]

\[\int\sqrt{2ax - x^2} \text{ dx}\]

\[\int\frac{1}{x\left( x - 2 \right) \left( x - 4 \right)} dx\]

\[\int\frac{\sin 2x}{\left( 1 + \sin x \right) \left( 2 + \sin x \right)} dx\]

\[\int\frac{5}{\left( x^2 + 1 \right) \left( x + 2 \right)} dx\]

\[\int\frac{1}{x \left( x^4 + 1 \right)} dx\]

\[\int\frac{1}{x^4 + 3 x^2 + 1} \text{ dx }\]

\[\int\frac{1}{\left( x - 1 \right) \sqrt{2x + 3}} \text{ dx }\]

\[\int\frac{x^3}{\sqrt{1 + x^2}}dx = a \left( 1 + x^2 \right)^\frac{3}{2} + b\sqrt{1 + x^2} + C\], then

\[\int\frac{x^4 + x^2 - 1}{x^2 + 1} \text{ dx}\]

\[\int\text{ cos x cos 2x cos 3x dx}\]

\[\int\frac{1}{\sqrt{x^2 - a^2}} \text{ dx }\]

\[\int\frac{\sin x}{\sqrt{\cos^2 x - 2 \cos x - 3}} \text{ dx }\]

\[\int\frac{1}{\sin^2 x + \sin 2x} \text{ dx }\]

\[\int\frac{1}{2 - 3 \cos 2x} \text{ dx }\]

\[\int\frac{\sin^5 x}{\cos^4 x} \text{ dx }\]

\[\int\frac{\sin^6 x}{\cos x} \text{ dx }\]

\[\int\frac{x^2}{x^2 + 7x + 10} dx\]

Notifications