Simple substitution
Task number: 3109
Calculate the following integrals and determine the intervals on which they are valid.
Variant 1
\(\int \root 3 \of {1- 3x} \, dx\)
Variant 2
\(\int \sin^7 x \cos x \, dx\)
Variant 3
\(\int x e^{-x^2} \, dx\)
Variant 4
\(\int \tan x \, dx\)
Variant 5
\(\int \cot x \, dx\)
Variant 6
\(\int \frac{x^2}{(1-x)^{100}} \, dx\)
Variant 7
\(\int \frac{x}{1 + x^4} \, dx\)
Variant 8
\(\int \frac{x^2}{\cos x^3} \, dx\)
Variant 9
\(\int \frac{1}{x \ln x} \, dx\)
Variant 10
\(\int \frac{2x + 1}{x^2 + x + 1} \, dx\)
Variant 11
\(\int \sin^{2k+1} x \, dx\) for \(k \in \mathbb N\)
Variant 12
\(\int \cos^{2k+1} x \, dx\) for \(k \in \mathbb N\)
Variant 13
\(\int \frac1{\sin x} \, dx\)
Variant 14
\(\int \frac{1}{\cos x} \, dx\)
