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

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

View Full Answer

Its FREE, you're just one step away


Subjective Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84
Enroll Now For FREE

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. $$\displaystyle\pm2\sqrt{\frac{\sin{\alpha}}{\alpha}}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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. $$x+ 3a \log x -\dfrac{3a^2}{x} - \dfrac{a^3}{2x^2}+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer