Mathematics

# Solve: $\displaystyle \int\dfrac{x + 2}{2x^2 + 6x + 5}dx$

$\frac{1}{4}log(2x^2+6x+5)+\frac{1}{2}tan^{-1}(2x+3)+C$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Single Correct Medium
If ${ I }_{ n }=\int { \sin ^{ n }{ x } dx },$, then ${ nI }_{ n }-\left( n-1 \right) { I }_{ n-2 }=$
• A. $\sin ^{ n-1 }{ x\cos { x } }$
• B. $\cos ^{ n-1 }{ x\sin{ x } }$
• C. $-\cos ^{ n-1 }{ x\sin{ x } }$
• D. $-\sin ^{ n-1 }{ x\cos { x } }$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
$\displaystyle \int\dfrac{{1-x^{}}}{1+x^{2}}$ dx

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$I = \int {{{{x^2}} \over {\sqrt {1 - {x^6}} }}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int x^{3}\tan ^{-1}x\:dx.$
• A. $\displaystyle \frac{1}{2}\left [ \left ( x^{4}-1 \right )\tan ^{-1}x-\frac{x^{2}}{3}+x \right ].$
• B. $\displaystyle \frac{1}{2}\left [ \left ( x^{4}+1 \right )\tan ^{-1}x-\frac{x^{2}}{3}+x \right ].$
• C. $\displaystyle \frac{1}{4}\left [ \left ( x^{4}-1 \right )\tan ^{-1}x-\frac{x^{1}}{3}+x \right ].$
• D. $\displaystyle \frac{1}{4}\left [ \left ( x^{4}-1 \right )\tan ^{-1}x-\frac{x^{2}}{3}+x \right ].$

Let $g(x)$ be a function defined on $[0, 7]$ and $g(x)=\int_0^x f(t) dt$, where $y=f(x)$ is the function whose graph is as shown in figure given below, then