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Find the integral $\int\frac{_1^2\left(3x^2+3x-12\right)}{6x^2+5x^2-6x}dx$

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Solution

Final Answer

$_1^2\left(\frac{3}{11}x+2\ln\left(x\right)-1.578512\ln\left(121x-66\right)\right)+C_0$
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Step-by-step Solution

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Simplify the expression inside the integral

$_1^2\int\frac{3x^2+3x-12}{11x^2-6x}dx$

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$_1^2\int\frac{3x^2+3x-12}{11x^2-6x}dx$

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Learn how to solve problems step by step online. Find the integral int((_1^2(3x^2+3x+-12))/(6x^2+5x^2-6x))dx. Simplify the expression inside the integral. Divide 3x^2+3x-12 by 11x^2-6x. Resulting polynomial. Expand the integral \int\left(\frac{3}{11}+\frac{\frac{51}{11}x-12}{11x^2-6x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.

Final Answer

$_1^2\left(\frac{3}{11}x+2\ln\left(x\right)-1.578512\ln\left(121x-66\right)\right)+C_0$

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 (_1^2(3x^2+3x)/(6x^2+5x^2))dx using partial fractionsSolve integral of (_1^2(3x^2+3x)/(6x^2+5x^2))dx using basic integralsSolve integral of (_1^2(3x^2+3x)/(6x^2+5x^2))dx using u-substitutionSolve integral of (_1^2(3x^2+3x)/(6x^2+5x^2))dx using integration by partsSolve integral of (_1^2(3x^2+3x)/(6x^2+5x^2))dx using trigonometric substitution

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Plotting: $_1^2\left(\frac{3}{11}x+2\ln\left(x\right)-1.578512\ln\left(121x-66\right)\right)+C_0$

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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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