Mathematics

# Evaluate the following integrals:$\displaystyle \int \dfrac{x^3}{2x + 1}dx$

$\dfrac{x^3}{6}-\dfrac{x^2}{8}+\dfrac{1}{8x}-\dfrac{1}{16}log(2x+1)+C$

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Single Correct Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

#### Realted Questions

Q1 Single Correct Hard
$\int \sqrt{\dfrac{cos x-cos^{3} x}{1-cos^{3} x}}$.dx is equal to

• A. $\dfrac{2}{3}sin^{-1}(cos^{3/2}x)+C$
• B. $\dfrac{3}{2}sin^{-1}(cos^{3/2}x)+C$
• C. none of these
• D. $\dfrac{2}{3}cos^{-1}(cos^{3/2}x)+C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Solve :

$\int\limits_0^a {\dfrac{{\sqrt x }}{{\sqrt x + \sqrt {a - x} }}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Obtain: $\int _{ a }^{ b }{ \sin { x } } dx$ as limit of sum.

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int e^x \sec x(1+\tan x)dx$
• A. $e^x\cos x+C$
• B. $e^x\sin x+C$
• C. $e^x\tan x+C$
• D. $e^x\sec x+C$

$\displaystyle \int_1^2(4x^3-5x^2+6x+9)dx$