Integration by parts
Task number: 3107
Calculate the following integrals. Don‘t forget to determine the interval on which the result is valid.
Variant 1
\(\int x \sin x \, dx\)
Variant 2
\(\int x^a \ln x \, dx\) (where \(a > 0\))
Variant 3
\(\int \frac{x^2}{e^x} \, dx\)
Variant 4
\(\int e^x \sin x \, dx\)
Variant 5
\(\int \ln x \, dx\)
Variant 6
\(\int \arcsin x \, dx \)
Variant 7
\(\int \arctan x \, dx\)
Variant 8
\(\int \sqrt{1-x^2} \, dx\)
