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  • Find the integral of <img alt="\int \frac{x+2}{2x^{2}+8x+3}dx" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cint%20%5Cfrac%7Bx&plus;2%7D%7B2x%5E%7B2%7D&plus;8x&plus;3%7Dd

Find the integral of \int \frac{x+2}{2x^{2}+8x+3}dx

Option: 1

\frac{1}{2}ln\left | 2x^{2}+8x+3 \right |+C


Option: 2

-\frac{1}{2}ln\left | 2x^{2}+8x+3 \right |+C


Option: 3

\frac{1}{4}ln\left | 2x^{2}+8x+3 \right |+C


Option: 4

-\frac{1}{4}ln\left | 2x^{2}+8x+3 \right |+C


Answers (1)

best_answer

Given integral,
\int \frac{x+2}{2x^{2}+8x+3}dx
Using the substitution method,
Let's assume,
u=2x^{2}+8x+3
du=4\left ( x+2 \right )dx
\left ( x+2 \right )dx=\frac{du}{4}
Now,
\int \frac{x+2}{2x^{2}+8x+3}dx=\int \frac{\frac{du}{4}}{u}
\int \frac{x+2}{2x^{2}+8x+3}dx=\frac{1}{4}\int \frac{du}{u}
\int \frac{x+2}{2x^{2}+8x+3}dx=\frac{1}{4}ln\left | u \right |+C
\int \frac{x+2}{2x^{2}+8x+3}dx=\frac{1}{4}ln\left | 2x^{2}+8x+3 \right |+C

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Gunjita

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