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Antiderivatives
Related Topics
Wize University Calculus 1 Textbook > Integrals
Antiderivatives of
1
x
\frac{1}{x}
x
1
3 Activities
Evaluate the following indefinite integral
∫
3
4
−
2
x
d
x
\displaystyle \int \frac{3}{4-2x} \ dx
∫
4
−
2
x
3
d
x
−
3
2
ln
∣
4
−
2
x
∣
+
C
\displaystyle\frac{-3}{2}\ln|4-2x|+C
2
−
3
ln
∣4
−
2
x
∣
+
C
3
2
ln
∣
(
4
−
2
x
)
∣
+
C
\displaystyle\frac{3}{2}\ln|(4-2x)|+C
2
3
ln
∣
(
4
−
2
x
)
∣
+
C
−
3
ln
∣
4
−
2
x
∣
+
C
\displaystyle{-3}\ln|4-2x|+C
−
3
ln
∣4
−
2
x
∣
+
C
3
ln
∣
2
x
∣
+
C
3\ln|2x|+C
3
ln
∣2
x
∣
+
C
I don't know
Check Submission
More Antiderivatives of
1
x
\frac{1}{x}
x
1
Questions:
Antiderivatives: Indefinite integrals
Evaluate the integral
∫
1
+
1
x
+
2
x
2
+
3
x
3
d
x
\displaystyle\int_{ }^{ }1+\frac{1}{x}+\frac{2}{x^2}+\frac{3}{x^3}dx
∫
1
+
x
1
+
x
2
2
+
x
3
3
d
x
.
Antiderivatives: Indefinite integrals
Evaluate the integral
∫
1
+
1
x
+
2
x
2
+
3
x
3
d
x
\displaystyle\int_{ }^{ }1+\frac{1}{x}+\frac{2}{x^2}+\frac{3}{x^3}dx
∫
1
+
x
1
+
x
2
2
+
x
3
3
d
x
.
Indefinite Integral
∫
(
x
−
2
+
x
−
1
+
1
+
x
+
x
2
)
d
x
\displaystyle \int_{ }^{ }\left(x^{-2}+x^{-1}+1+x+x^2\right)dx
∫
(
x
−
2
+
x
−
1
+
1
+
x
+
x
2
)
d
x
Practice: Long Division First
Q
:
\bf{Q:}
Q
:
Evaluate
∫
x
3
−
x
2
−
x
−
3
x
−
2
d
x
\displaystyle\int_{ }^{ }\frac{x^3-x^2-x-3}{x-2}dx
∫
x
−
2
x
3
−
x
2
−
x
−
3
d
x
Practice: Long Division First
Evaluate
∫
x
3
−
x
2
−
x
−
3
x
−
2
d
x
\displaystyle\int_{ }^{ }\frac{x^3-x^2-x-3}{x-2}dx
∫
x
−
2
x
3
−
x
2
−
x
−
3
d
x
(a)
x
3
3
+
x
2
2
+
x
−
ln
∣
x
−
2
∣
+
C
\frac{x^3}{3}+\frac{x^2}{2}+x-\ln\left|x-2\right|+C
3
x
3
+
2
x
2
+
x
−
ln
∣
x
−
2
∣
+
C
(b)
1
2
x
2
−
3
ln
∣
x
−
2
∣
+
C
\frac12x^2-3\ln\left|x-2\right|+C
2
1
x
2
−
3
ln
∣
x
−
2
∣
+
C
(c)
=
x
3
3
+
x
2
2
+
x
−
1
2
(
x
−
2
)
2
+
C
=\frac{x^3}{3}+\frac{x^2}{2}+x-\frac12(x-2)^2+C
=
3
x
3
+
2
x
2
+
x
−
2
1
(
x
−
2
)
2
+
C
Practice: Indefinite Integral
Evaluate the integral
∫
x
+
1
+
1
x
+
2
x
2
d
x
\displaystyle\int_{ }^{ }x+1+\frac{1}{x}+\frac{2}{x^2}dx
∫
x
+
1
+
x
1
+
x
2
2
d
x
Practice: Indefinite Integral
Evaluate the integral
∫
1
+
1
x
+
2
x
2
+
3
x
3
d
x
\displaystyle\int_{ }^{ }1+\frac{1}{x}+\frac{2}{x^2}+\frac{3}{x^3}dx
∫
1
+
x
1
+
x
2
2
+
x
3
3
d
x
.
Practice: Long Division First
Q
:
\bf{Q:}
Q
:
Evaluate
∫
x
3
−
x
2
−
x
−
3
x
−
2
d
x
\displaystyle\int_{ }^{ }\frac{x^3-x^2-x-3}{x-2}dx
∫
x
−
2
x
3
−
x
2
−
x
−
3
d
x
Antiderivatives: Indefinite integrals
Evaluate the integral
∫
1
+
1
x
+
2
x
2
+
3
x
3
d
x
\displaystyle\int_{ }^{ }1+\frac{1}{x}+\frac{2}{x^2}+\frac{3}{x^3}dx
∫
1
+
x
1
+
x
2
2
+
x
3
3
d
x
.
Indefinite Integral
∫
(
x
−
2
+
x
−
1
+
1
+
x
+
x
2
)
d
x
\displaystyle \int_{ }^{ }\left(x^{-2}+x^{-1}+1+x+x^2\right)dx
∫
(
x
−
2
+
x
−
1
+
1
+
x
+
x
2
)
d
x