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Find the integral $\int\frac{2x^2}{5x-1}dx$

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Solution

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Final Answer

$\frac{1}{5}x^2+\frac{2}{25}x+\frac{2}{125}\ln\left(5x-1\right)+C_0$
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Step-by-step Solution

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Take out the constant $2$ from the integral

$2\int\frac{x^2}{5x-1}dx$

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$2\int\frac{x^2}{5x-1}dx$

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Learn how to solve differential calculus problems step by step online. Find the integral int((2x^2)/(5x-1))dx. Take out the constant 2 from the integral. Divide x^2 by 5x-1. Resulting polynomial. Expand the integral \int\left(\frac{1}{5}x+\frac{1}{25}+\frac{1}{25\left(5x-1\right)}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately.

Final Answer

$\frac{1}{5}x^2+\frac{2}{25}x+\frac{2}{125}\ln\left(5x-1\right)+C_0$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve integral of (2x^2/(5x-1))dx using partial fractionsSolve integral of (2x^2/(5x-1))dx using basic integralsSolve integral of (2x^2/(5x-1))dx using u-substitutionSolve integral of (2x^2/(5x-1))dx using integration by partsSolve integral of (2x^2/(5x-1))dx using trigonometric substitution

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Function Plot

Plotting: $\frac{1}{5}x^2+\frac{2}{25}x+\frac{2}{125}\ln\left(5x-1\right)+C_0$

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5
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7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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$\frac{d}{dx}\left(2x+1\right)$

Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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