Math  /  Calculus

QuestionFind dud u and uu \begin{tabular}{|l|} \hline 6. Arctanxdx\int \operatorname{Arctan} x d x \\ \hline 7. Arcsin2xdx14x2\int \frac{\operatorname{Arcsin} 2 x d x}{\sqrt{1-4 x^{2}}} \\ \hline 8. xcsc(1x2)cot(1x2)dx\int x \csc \left(1-x^{2}\right) \cot \left(1-x^{2}\right) d x \\ \hline 9. 10cosxecosxsinxdx\int 10^{\cos x} e^{\cos x} \sin x d x \\ \hline 10x3e2xdx10 \int x^{3} e^{2 x} d x \\ \hline \end{tabular}

Studdy Solution
For x3e2xdx\int x^3 e^{2x} \, dx, use integration by parts: Let u=x3 u = x^3 and dv=e2xdx dv = e^{2x} \, dx .
Then, du=3x2dx du = 3x^2 \, dx and v=12e2x v = \frac{1}{2}e^{2x} .

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