Question

Помогите решить неопределенные интегралы

Answer 1

$\int\frac{(3+7x^4)dx}{x}=3\int\frac{dx}{x}+7\int x^3dx=3ln|x|+\frac{7x^4}{4}+C$
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$\int(3x^3*e^{2-x^4})dx=-\frac{3}{4}\int e^{2-x^4}d(2-x^4)=-\frac{3}{4}e^{2-x^4}+C$
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$\int\frac{xdx}{\sqrt{3-x^4}}=\frac{1}{2}\int\frac{d(x^2)}{\sqrt{3-x^4}}=\frac{1}{2}arcsin\frac{x^2}{\sqrt3}+C$
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$\int (x^2sinx)dx=-x^2cosx+2\int xcosx=-x^2cosx+2xsinx+2cosx+C\\\\\\u=x^2=\ \textgreater \ du=2x\\dv=sinxdx=\ \textgreater \ v=-cosx\\\\\\\int xcosx=xsinx-\int sinxdx=xsinx+cosx\\p=x=\ \textgreater \ dp=dx\\dq=cosx=\ \textgreater \ q=sinx$