Mathematics

# Evaluate$\int { x-3 } \sqrt { { x }^{ 2 }+4x+3 } dx$

##### SOLUTION
$\displaystyle\int \sqrt{x^{2}+4{x}+3}dx=\displaystyle\int \sqrt{(x+2)^{2}-1}\ dx=\dfrac{(x+2)}{2}\sqrt{(x+2)^{2}-1}-\dfrac{1}{2}\ln \mid (x+2)+\sqrt{(x+2)^{2}-1}\ \mid$
$\displaystyle\int (x-3\sqrt{x^{2}+4{x}+3})dx=\ \dfrac{x^{2}}{2}-\dfrac{3}{2}(x+2)\sqrt{x^{2}+4{x}+3}+\dfrac{3}{2}\ln \mid x+2+\sqrt{x^{2}+4{x}+3} \ \mid+C$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114

#### Realted Questions

Q1 Single Correct Medium
The function f(x) satisfying the equation ${f^2}\left( x \right) + 4f\left( x \right) \cdot f'\left( x \right) + {\left[ {f'\left( x \right)} \right]^2} = 0$ is
• A. $f\left( x \right) = c.{e^{\left( {2 + \sqrt 3 } \right)x}}$
• B. $f\left( x \right) = c.{e^{\left( {\sqrt 3 - 2} \right)x}}$
• C. $f\left( x \right) = c.{e^{ - \left( {2 + \sqrt 3 } \right)x}}$
• D. $f\left( x \right) = c.{e^{\left( {2 - \sqrt 3 } \right)x}}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\int {\frac{{{{\sin }^{ - 1}}x}}{{{{\left( {1 - {x^2}} \right)}^{\frac{3}{2}}}}}dx}$
• A. $\frac{1}{2}\log \left| {\left( {1 - {x^2}} \right)} \right| + C$
• B. $\frac{{x\left( {{{\sin }^{ - 1}}x} \right)}}{{\sqrt {1 - {x^2}} }}+C$
• C. $4+\frac { \pi }{ 2 }$
• D. $\frac{{x\left( {{{\sin }^{ - 1}}x} \right)}}{{\sqrt {1 - {x^2}} }} + \frac{1}{2}\log \left| {\left( {1 - {x^2}} \right)} \right| + C.$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Integrate the function    $(x^2+1)\log x$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve $\displaystyle\int {\dfrac{1}{{{x^5}}}\left( {1 + {x^4}} \right)dx}$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\displaystyle \int x\{f(x^{2}) g' (x^{2})+f '(x^{2})g(x^{2})\}dx$ is equal to
• A. $f(x^{2}) g$' $(x^{2})-g(x^{2}) f$'$(x^{2})+c$
• B. ${\dfrac{1}{2}}\{f(x^{2})g(x^{2}) f$' $(x^{2})\}+c$
• C. ${\dfrac{1}{2}}\{f(x^{2}) g$' $(x^{2})-g(x^{2}) f$' $(x^{2})\}+c$
• D. ${\dfrac{1}{2}} [f(x^{2})g(x^{2})]+c$