Mathematics

# Evaluate $\displaystyle\int \dfrac {x^3+4x^2+9x}{x^2+4x+9} dx$

##### SOLUTION
$\displaystyle\int \dfrac {x^3+4x^2+9x}{x^2+4x+9} dx\\\displaystyle \int \dfrac{x(x^2+4x+9)}{x^2+4x+9}dx\\\displaystyle \int x dx\\\dfrac{x^2}{2}+c$

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Multiple Correct Hard
Let $f(x) = 7\tan^8x+7\tan^6x-3\tan^4x-3\tan^2x$ for all $x\in\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)$, then the correct expression(s) is (are)
• A. $\displaystyle \int_0^{\dfrac{\pi}{4}}xf(x)dx = \dfrac{1}{6}$
• B. $\displaystyle \int_0^{\dfrac{\pi}{4}}xf(x)dx =1$
• C. $\displaystyle \int_0^{\dfrac{\pi}{4}}xf(x)dx = \dfrac{1}{12}$
• D. $\displaystyle \int_0^{\dfrac{\pi}{4}}f(x)dx = 0$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Find F (x) from the given F'(x)
F'(x) = $7x^2$ - 2x + 3, whose graph passes through the point M(1, 5).

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
The integral $\int_{\pi /4}^{\pi / 2}(2cosec x)^{17}dx$ is equal to
• A. $\int_{0}^{\log(1 + \sqrt {2})} 2(e^{u} + e^{-u})^{17}du$
• B. $\int_{0}^{\log(1 + \sqrt {2})} 2(e^{u} - e^{-u})^{17}du$
• C. $\int_{0}^{\log(1 + \sqrt {2})} 2(e^{u} - e^{-u})^{16}du$
• D. $\int_{0}^{\log(1 + \sqrt {2})} 2(e^{u} + e^{-u})^{16}du$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Evaluate the given integral.
$\displaystyle \int { { e }^{ x } } \left( \log { x } +\cfrac { 1 }{ { x }^{ 2 } } \right) dx$

Evaluate $\displaystyle \int { \dfrac { 1-4x }{ \sqrt { 6+x-{ 2x }^{ 2 } } } } dx$