Mathematics

# Evaluate : $\displaystyle \int x^2+3x+5\ dx$

##### SOLUTION

$\displaystyle \int x^2+3x+5\ dx$

$=\displaystyle \int x^2 dx+\int 3x dx+\int 5 dx$

we know that $\displaystyle\int{{x}^{n}dx}=\dfrac{{x}^{n+1}}{n+1}+c$

$=\dfrac {x^3}{3}+\dfrac {3x^2}{2}+5x+c$

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

#### Realted Questions

Q1 Single Correct Hard
If $x$ satisfies the equation $\displaystyle\left(\int_0^1{\frac{dt}{t^2+2t\cos{\alpha}+1}}\right)x^2-\left(\int_{-3}^3{\frac{t^2\sin{2t}}{t^2+1}dt}\right)x-2=0$
for $(0<\alpha<\pi)$
then the value of $x$ is?
• A. $\displaystyle\pm\sqrt{\frac{\alpha}{2\sin{\alpha}}}$
• B. $\displaystyle\pm\sqrt{\frac{2\sin{\alpha}}{\alpha}}$
• C. $\displaystyle\pm\sqrt{\frac{\alpha}{\sin{\alpha}}}$
• D. $\displaystyle\pm2\sqrt{\frac{\sin{\alpha}}{\alpha}}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Solve : $\displaystyle \int$ sin 2x dx

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate $\int _ { - 5 } ^ { 5 } | x + 2 | d x$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
The value of $\displaystyle \int_{-2\pi}^{5\pi} \cot^{-1}(\tan x) dx$ is equal to:
• A. $\dfrac{7\pi}{2}$
• B. $\dfrac{7\pi^{2}}{2}$
• C. $\dfrac{3\pi}{2}$
• D. None of these

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$I=\displaystyle \int \dfrac{(x+a)^3}{x^3}dx$ is equal to:
• A. $x^2+ 3a \log x -\dfrac{3a^2}{x} - \dfrac{a^3}{2x^2}+c$
• B. $x^3+ 3a \log x -\dfrac{2a^2}{x} - \dfrac{3a^3}{2x^2}+c$
• C. $1+ 2a \log x -\dfrac{2a^2}{x} - \dfrac{3a^2}{2x^2}+c$
• D. $x+ 3a \log x -\dfrac{3a^2}{x} - \dfrac{a^3}{2x^2}+c$