English

CBSECommerce (English Medium) Class 12

Question Papers

Question Papers2489

Textbook Solutions20216

MCQ Online Mock Tests42

Important Solutions18873

Concept Notes & Videos242

∫ X + 1 √ 2 X + 3 D X - Mathematics

Advertisements

Advertisements

Question

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

Sum

Solution

\[\int\left( \frac{x + 1}{\sqrt{2x + 3}} \right)dx\]
\[ = \frac{1}{2}\int\left( \frac{2x + 2}{\sqrt{2x + 3}} \right)dx\]
\[ = \frac{1}{2}\int\left( \frac{2x + 3 - 1}{\sqrt{2x + 3}} \right)dx\]
\[ = \frac{1}{2}\int\left( \frac{2x + 3}{\sqrt{2x + 3}} - \frac{1}{\sqrt{2x + 3}} \right)dx\]
\[ = \frac{1}{2}\int\left( \sqrt{2x + 3} - \frac{1}{\sqrt{2x + 3}} \right)dx\]
\[ = \frac{1}{2}\left[ \int \left( 2x + 3 \right)^\frac{1}{2} dx - \int \left( 2x + 3 \right)^{- \frac{1}{2}} dx \right]\]
\[ = \frac{1}{2}\left[ \frac{\left( 2x + 3 \right)^\frac{1}{2} + 1}{2\left( \frac{1}{2} + 1 \right)} - \frac{\left( 2x + 3 \right)^{- \frac{1}{2} + 1}}{2\left( - \frac{1}{2} + 1 \right)} + C \right]\]
\[ = \frac{1}{2}\left[ \frac{1}{3} \left( 2x + 3 \right)^\frac{3}{2} - \left( 2x + 3 \right)^\frac{1}{2} + C \right]\]
\[ = \frac{1}{6} \left( 2x + 3 \right)^\frac{3}{2} - \frac{1}{2} \left( 2x + 3 \right)^\frac{1}{2} + C\]

shaalaa.com

Indefinite Integral Problems

Is there an error in this question or solution?

Chapter 19: Indefinite Integrals - Exercise 19.05 [Page 33]

APPEARS IN

RD Sharma Mathematics [English] Class 12

Chapter 19 Indefinite Integrals
Exercise 19.05 | Q 1 | Page 33

Video TutorialsVIEW ALL [1]

view
Video Tutorials For All Subjects
Indefinite Integral Problems

video tutorial00:39:37

RELATED QUESTIONS

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

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

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

\[\int\frac{1}{\sqrt{x + a} + \sqrt{x + b}} dx\]

\[\int\frac{e^{3x}}{e^{3x} + 1} dx\]

` ∫ {sec x "cosec " x}/{log ( tan x) }` dx

\[\int\frac{\cos x}{2 + 3 \sin x} dx\]

\[\int\frac{\sin 2x}{\sin 5x \sin 3x} dx\]

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

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

\[\int \cot^n {cosec}^2 \text{ x dx } , n \neq - 1\]

\[\int\frac{\cos x}{\sin^2 x + 4 \sin x + 5} dx\]

\[\int\frac{\sec^2 x}{\sqrt{4 + \tan^2 x}} dx\]

\[\int\frac{\cos x}{\sqrt{4 + \sin^2 x}} dx\]

\[\int\frac{x}{\sqrt{8 + x - x^2}} dx\]

\[\int\frac{2x + 5}{\sqrt{x^2 + 2x + 5}} dx\]

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

\[\int\frac{\sin 2x}{\sin^4 x + \cos^4 x} \text{ dx }\]

`int 1/(cos x - sin x)dx`

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

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

\[\int e^x \sec x \left( 1 + \tan x \right) dx\]

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

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

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

\[\int\frac{3x + 5}{x^3 - x^2 - x + 1} dx\]

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

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

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

\[\int\frac{1}{1 + \tan x} dx =\]

\[\int \sec^2 x \cos^2 2x \text{ dx }\]

\[\int \tan^3 x\ dx\]

\[\int \cot^4 x\ dx\]

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

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

\[\int\frac{1}{5 - 4 \sin x} \text{ dx }\]

\[\int\frac{1}{x \sqrt{1 + x^n}} \text{ dx}\]

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

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

Find : \[\int\frac{dx}{\sqrt{3 - 2x - x^2}}\] .

Notifications