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Realted Questions

Q1 Subjective Medium
Evaluate:
$$\displaystyle \int \dfrac { x ^ { 3 } } { ( x + 1 ) ^ { 2 } } d x$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Single Correct Medium
$$\displaystyle\int { \dfrac { \left( 1+x \right) { e }^{ x } }{ \cot { \left( x{ e }^{ x } \right)  }  } dx } $$ is equal to
  • A. $$\log { \left| \cos { \left( x{ e }^{ x } \right) } \right| } +C$$
  • B. $$\log { \left| \cot { \left( x{ e }^{ x } \right) } \right| } +C$$
  • C. $$\log { \left| \cos { \left( x{ e }^{ -x } \right) } \right| } +C$$
  • D. $$\log { \left| \sec { \left( x{ e }^{ x } \right) } \right| } +C$$
  • E. $$\log { \left| \sec { \left( x{ e }^{ -x } \right) } \right| } +C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Single Correct Hard
Evaluate : $$\displaystyle \int \frac{\left ( 4x+1 \right )\; dx}{x^{2}+3x+2}$$ 
  • A. $$\displaystyle=2\:log\left | x^{2}+5x+2 \right |-5log\left | \frac{x+1}{x+2} \right |+C$$
  • B. $$\displaystyle=2\:log\left | x^{2}+3x+2 \right |-5log\left | \frac{x+3}{x+2} \right |+C$$
  • C. $$\displaystyle=2\:log\left | x^{2}+3x+2 \right |-5log\left | \frac{x+1}{x+3} \right |+C$$
  • D. $$\displaystyle=2\:log\left | x^{2}+3x+2 \right |-5log\left | \frac{x+1}{x+2} \right |+C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Subjective Medium
Prove that: $$\displaystyle\int^1_{-1}(ax^3+bx)dx=0$$ .

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Subjective Medium
Find $$\int a^{x} \cdot e^{x} dx$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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