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# Integrate $\int\left(-21x+\frac{1}{x}\right)dx$

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ln
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asin
acos
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sinh
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asinh
acosh
atanh
acoth
asech
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##  Final answer to the problem

$-\frac{21}{2}x^2+\ln\left(x\right)+C_0$
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##  Step-by-step Solution 

Specify the solving method

1

Expand the integral $\int\left(-21x+\frac{1}{x}\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\int-21xdx+\int\frac{1}{x}dx$

Learn how to solve integrals of polynomial functions problems step by step online.

$\int-21xdx+\int\frac{1}{x}dx$

Learn how to solve integrals of polynomial functions problems step by step online. Integrate int(-21x+1/x)dx. Expand the integral \int\left(-21x+\frac{1}{x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int-21xdx results in: -\frac{21}{2}x^2. The integral \int\frac{1}{x}dx results in: \ln\left(x\right). Gather the results of all integrals.

##  Final answer to the problem

$-\frac{21}{2}x^2+\ln\left(x\right)+C_0$

##  Explore different ways to solve this problem

SnapXam A2

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7
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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
Dx
|◻|
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

###  Main Topic: Integrals of Polynomial Functions

Integrals of polynomial functions.