Mathematics

# $\int 5 ^ { 5 ^ { 5 x } } \cdot 5 ^ { 5 x } 5 ^ { x } d x$ is equal to ________.

$\dfrac { 5 ^ { 5 ^ { 5 x } } } { ( \log 5 ) ^ { 3 } } + c$

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

#### Realted Questions

Q1 Subjective Hard
Prove that

$\displaystyle \int {\dfrac{{{{\sin }^{ - 1}}x}}{{{{\left( {1 - {x^2}} \right)}^{\dfrac{3}{2}}}}}} dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
The value of $\displaystyle \int_0^{\cfrac {\pi}{2}}\log \left (\frac {4+3 \sin x}{4+3 \cos x}\right )dx$ is
• A. $2$
• B. $\frac {3}{4}$
• C. $-2$
• D. $0$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Solve:
$\int { \dfrac { dx }{ 2{ x }^{ 2 }+x-1 } }$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate $\displaystyle \int_{1}^{2}x^2 \ dx$

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Hard
Let us consider the integral of the following forms
$f{(x_1,\sqrt{mx^2+nx+p})}^{\tfrac{1}{2}}$
Case I If $m>0$, then put $\sqrt{mx^2+nx+C}=u\pm x\sqrt{m}$
Case II If $p>0$, then put $\sqrt{mx^2+nx+C}=u\pm \sqrt{p}$
Case III If quadratic equation $mx^2+nx+p=0$ has real roots $\alpha$ and $\beta$, then put $\sqrt{mx^2+nx+p}=(x-\alpha)u\:or\:(x-\beta)u$