Mathematics

# Evaluate: $\displaystyle \int (x^3+5x^2+6)(3x^2+5x)d x$

##### SOLUTION

$\displaystyle \int (x^3+5x^2+6)(3x^2+5x)d x \\t=x^3+5x^2+6\implies 3x^2+5x dx =dt \\\displaystyle\int tdt\\\dfrac{t^2}{2}+c\\\dfrac{x^3+5x^2+6}{2}+c$

Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Single Correct Medium
$\displaystyle\int \dfrac{1}{4x^2+4x+3}dx=?$
• A. $\dfrac{1}{2\sqrt{2}}\tan^{-1}\left(\dfrac{2x+1}{\sqrt{2}}\right)+C$
• B. $\dfrac{1}{2}\tan^{-1}(2x-1)+C$
• C. $\dfrac{1}{2}\tan^{-1}(2x+1)+C$
• D. $\dfrac{1}{2\sqrt{2}}\tan^{-1}\left(\dfrac{2x-1}{\sqrt{2}}\right)+C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
If $\displaystyle \int_{1/4}^{x}\displaystyle \frac{dt}{\sqrt{t-t^{2}}}= \displaystyle \frac{\pi }{6}$, then $x$ equals
• A. $1/3$
• B. $1$
• C. none of these
• D. $1/2$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If the anti-derivative of $\displaystyle \int \frac{\sin^4 x}{x} dx$ is $f(x)$, then $\displaystyle \int \frac{\sin^4 \{ (p + q)x \}}{x} dx$ in terms of $f(x)$ is
• A. $\frac{f \{ (p + q)x \}}{p + q}$
• B. $f \{ (p + q)x \} (p + q)$
• C. None of these
• D. $f \{ (p + q)x \}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate : $\int _ { \log 1 / 2 } ^ { \log 2 } \sin \left( \dfrac { e ^ { x } - 1 } { e ^ { x } + 1 } \right) d x$

Integrate $\displaystyle \int \dfrac 1{\sqrt {3-x^2}}dx$