English

CBSECommerce (English Medium) Class 12

Question Papers

Question Papers2890

Textbook Solutions20276

MCQ Online Mock Tests42

Important Solutions23871

Concept Notes & Videos601

Ed∫x+3(x+4)2ex dx = ______.

Advertisements

Advertisements

Question

`int (x + 3)/(x + 4)^2 "e"^x "d"x` = ______.

Fill in the Blanks

Advertisements

Solution

`int (x + 3)/(x + 4)^2 "e"^x "d"x` = `"e"^x/(x + 4) + "C"`.

Explanation:

Let I = `int (x + 3)/(x + 4)^2 * "e"^x "d"x`

= `int (x + 4 - 1)/(x + 4)^2 * "e"^x "d"x`

= `int [(x + 4)/(x + 4)^2 - 1/(x + 4)^2]"e"^x "d"x`

= `int [1/(x + 4) - 1/(x + 4)^2]"e"^x "d"x`

Put `1/(x + 4)` = t

⇒ `- 1/(x + 4)^2 "d"x` = dt

Let f(x) = `1/(x + 4)`

∴ f'(x) = `- 1/(x + 4)^2`

Using `int "e"^x ["f"(x) + "f'"(x)]"d"x = "e"^x "f"(x) + "C"`

∴ I = `"e"^x * 1/(x + 4) + "C"`.

shaalaa.com

Definite Integrals

Is there an error in this question or solution?

Chapter 7: Integrals - Exercise [Page 169]

APPEARS IN

NCERT Exemplar Mathematics Exemplar [English] Class 12

Chapter 7 Integrals
Exercise | Q 60 | Page 169

RELATED QUESTIONS

\[\int\limits_0^1 \frac{x}{x + 1} dx\]

\[\int\limits_0^{\pi/2} \sin x \sin 2x\ dx\]

\[\int\limits_0^{\pi/2} \left( a^2 \cos^2 x + b^2 \sin^2 x \right) dx\]

\[\int\limits_0^{\pi/2} \sqrt{1 + \sin x}\ dx\]

\[\int\limits_0^{\pi/2} \sqrt{1 + \cos x}\ dx\]

\[\int\limits_0^1 x \tan^{- 1} x\ dx\]

\[\int\limits_0^{\pi/2} x^2 \sin\ x\ dx\]

\[\int\limits_0^{\pi/2} \sin 2x \tan^{- 1} \left( \sin x \right) dx\]

\[\int\limits_0^a \sin^{- 1} \sqrt{\frac{x}{a + x}} dx\]

\[\int\limits_0^a x \sqrt{\frac{a^2 - x^2}{a^2 + x^2}} dx\]

\[\int_0^\frac{\pi}{4} \frac{\sin^2 x \cos^2 x}{\left( \sin^3 x + \cos^3 x \right)^2}dx\]

\[\int\limits_0^{\pi/2} \left( 2 \log \cos x - \log \sin 2x \right) dx\]

\[\int\limits_0^{\pi/2} \frac{\sqrt{\cot x}}{\sqrt{\cot x} + \sqrt{\tan x}} dx\]

\[\int\limits_0^{\pi/2} \frac{\sin^{3/2} x}{\sin^{3/2} x + \cos^{3/2} x} dx\]

\[\int\limits_0^\pi \frac{x \sin x}{1 + \sin x} dx\]

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

If f(2a − x) = −f(x), prove that

\[\int\limits_0^{2a} f\left( x \right) dx = 0 .\]

\[\int\limits_0^2 \left( x^2 + x \right) dx\]

\[\int\limits_0^{\pi/2} \sin^2 x\ dx .\]

\[\int\limits_{- \pi/2}^{\pi/2} x \cos^2 x\ dx .\]

\[\int\limits_0^{\pi/2} \sqrt{1 - \cos 2x}\ dx .\]

\[\int\limits_0^\pi \cos^5 x\ dx .\]

If \[\left[ \cdot \right] and \left\{ \cdot \right\}\] denote respectively the greatest integer and fractional part functions respectively, evaluate the following integrals:

\[\int\limits_0^{\pi/4} \sin \left\{ x \right\} dx\]

\[\int\limits_0^{\pi/4} \sin 2x \sin 3x dx\]

\[\int\limits_0^1 \left| \sin 2\pi x \right| dx\]

\[\int\limits_0^{\pi/2} \frac{\cos^2 x}{\sin x + \cos x} dx\]

\[\int\limits_0^1 \cot^{- 1} \left( 1 - x + x^2 \right) dx\]

\[\int\limits_0^4 x dx\]

\[\int\limits_1^4 \left( x^2 + x \right) dx\]

\[\int\limits_2^3 e^{- x} dx\]

\[\int\limits_1^3 \left( 2 x^2 + 5x \right) dx\]

\[\int\limits_1^3 \left( x^2 + 3x \right) dx\]

Evaluate the following:

`Γ (9/2)`

Find `int x^2/(x^4 + 3x^2 + 2) "d"x`

Evaluate `int "dx"/sqrt((x - alpha)(beta - x)), beta > alpha`

If `int (3"e"^x - 5"e"^-x)/(4"e"6x + 5"e"^-x)"d"x` = ax + b log |4e^x + 5e –x| + C, then ______.

If x = `int_0^y "dt"/sqrt(1 + 9"t"^2)` and `("d"^2y)/("d"x^2)` = ay, then a equal to ______.

Notifications