Mathematics

# solve:$\displaystyle \int { {\dfrac{n}{{1 - {n^2}}}} dn}$

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

#### Realted Questions

Q1 Subjective Hard

If the equation $a{x^2} + bx + c = 0$ does not have $2$ distinct real
roots and $a + c > b,$ then prove that $\int {\left( x \right)} \ge 0,\forall x \in R.$

1 Verified Answer | Published on 17th 09, 2020

Q2 TRUE/FALSE Medium
State whether the given statement is true or false
the value of the integral $\displaystyle \int_{0}^{2a}\frac{f\left ( x \right )}{f\left ( x \right )+f\left ( 2a-x \right )}dx$ is equal to a.
• A. False
• B. True

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Integrate $\displaystyle\int { \dfrac { { x }^{ 2 }dx }{ { x }^{ 6 }-{ a }^{ 6 } } dx }$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Evaluate : $\displaystyle \int_{- \pi}^{\pi} \dfrac{\sin^2 x}{1 + e^x}dx$

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 $\displaystyle f(x)>0 \forall x \in R$