Advertisements
Advertisements
Question
\[\int \left( 3x + 4 \right)^2 dx\]
Sum
Advertisements
Solution
\[\int \left( 3x + 4 \right)^2 dx\]
\[ = \int \left( 9 x^2 + 2 \times 3x \times 4 + 16 \right)dx\]
`= 9 ∫ x^2dx + 24 ∫ x dx + 16 ∫ dx`
\[ = 9\left[ \frac{x^3}{3} \right] + 24\left[ \frac{x^2}{2} \right] + 16x + C\]
\[ = 3 x^3 + 12 x^2 + 16x + C\]
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int \cos^{- 1} \left( \sin x \right) dx\]
If f' (x) = x − \[\frac{1}{x^2}\] and f (1) \[\frac{1}{2}, find f(x)\]
If f' (x) = a sin x + b cos x and f' (0) = 4, f(0) = 3, f
\[\left( \frac{\pi}{2} \right)\] = 5, find f(x)
\[\int\frac{1}{\sqrt{2x + 3} + \sqrt{2x - 3}} dx\]
\[\int\frac{1}{\sqrt{x + a} + \sqrt{x + b}} dx\]
\[\int \text{sin}^2 \left( 2x + 5 \right) \text{dx}\]
\[\int \cos^2 \text{nx dx}\]
\[\int\frac{- \sin x + 2 \cos x}{2 \sin x + \cos x} dx\]
\[\int\frac{x \sin^{- 1} x^2}{\sqrt{1 - x^4}} dx\]
\[\int\frac{1}{1 + x - x^2} \text{ dx }\]
\[\int\frac{1}{x \left( x^6 + 1 \right)} dx\]
\[\int\frac{\cos x}{\sqrt{\sin^2 x - 2 \sin x - 3}} dx\]
\[\int\frac{\left( 3 \sin x - 2 \right) \cos x}{5 - \cos^2 x - 4 \sin x} dx\]
\[\int\frac{\left( 1 - x^2 \right)}{x \left( 1 - 2x \right)} \text
{dx\]
\[\int\frac{x^2 + x + 1}{x^2 - x + 1} \text{ dx }\]
\[\int\frac{3x + 1}{\sqrt{5 - 2x - x^2}} \text{ dx }\]
\[\int\frac{1}{5 + 4 \cos x} dx\]
\[\int\frac{1}{1 - \sin x + \cos x} \text{ dx }\]
\[\int\frac{1}{2 + \sin x + \cos x} \text{ dx }\]
\[\int\frac{8 \cot x + 1}{3 \cot x + 2} \text{ dx }\]
\[\int \sin^{- 1} \sqrt{x} \text{ dx }\]
\[\int x^2 \sin^{- 1} x\ dx\]
\[\int \cos^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right) \text{ dx }\]
\[\int e^x \left( \tan x - \log \cos x \right) dx\]
\[\int\frac{\sqrt{1 - \sin x}}{1 + \cos x} e^{- x/2} \text{ dx }\]
\[\int\left( 2x - 5 \right) \sqrt{x^2 - 4x + 3} \text{ dx }\]
\[\int\frac{1}{x \log x \left( 2 + \log x \right)} dx\]
\[\int\frac{1}{x\left( x^n + 1 \right)} dx\]
Find \[\int\frac{2x}{\left( x^2 + 1 \right) \left( x^2 + 2 \right)^2}dx\]
\[\int\frac{1}{\sin x + \sin 2x} dx\]
\[\int\frac{\cos 2x - 1}{\cos 2x + 1} dx =\]
\[\int\frac{x^3}{x + 1}dx\] is equal to
\[\int\frac{\sin 2x}{a^2 + b^2 \sin^2 x}\]
\[\int \tan^3 x\ dx\]
\[\int \tan^5 x\ \sec^3 x\ dx\]
\[\int x^3 \left( \log x \right)^2\text{ dx }\]
\[\int\frac{x^5}{\sqrt{1 + x^3}} \text{ dx }\]
\[\int\frac{x^2}{x^2 + 7x + 10}\text{ dx }\]
