Mathematics

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


SOLUTION

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

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

$$I=\dfrac {x^3}{3}+\dfrac {3x^2}{2}+5x+c$$
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 Medium
What is $$\displaystyle \int_0^1 {\frac{\tan^{-1}x}{1 + x^2} dx}$$ equal to ?
  • A. $$\dfrac{\pi}{4}$$
  • B. $$\dfrac{\pi}{8}$$
  • C. $$\dfrac{\pi^2}{8}$$
  • D. $$\dfrac{\pi^2}{32}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
Evaluate the definite integral   $$\displaystyle \int_0^1\frac {dx}{\sqrt {1+x}-\sqrt x}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Multiple Correct Medium
The value of $$\displaystyle \int_{0}^{1} \dfrac{2 x^{2}+3 x+3}{(x+1)\left(x^{2}+2 x+2\right)} d x$$ is
  • A. $$\dfrac{\pi}{4}+2 \log 2-\tan ^{-1} \dfrac{1}{3}$$
  • B. $$\dfrac{\pi}{4}+2 \log 2-\tan ^{-1} 2$$
  • C. $$2 \log 2-\cot ^{-1} 3$$
  • D. $$-\dfrac{\pi}{4}+\log 4+\cot ^{-1} 2$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Medium
Integrate the function:  $$\cfrac{\sin ^{-1} x}{\sqrt{1-x^{2}}}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Passage Medium
Consider two differentiable functions $$f(x), g(x)$$ satisfying $$\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$$ & $$\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$$. where $$\displaystyle f(x)>0    \forall  x \in  R$$

On the basis of above information, answer the following questions :

Asked in: Mathematics - Limits and Derivatives


1 Verified Answer | Published on 17th 08, 2020

View Answer