What is expand ln(a+1)*(e^a+a*e^a) ?

The solution to expand ln(a+1)*(e^a+a*e^a) is e^aln(a+1)+ae^aln(a+1)

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expand ln(a+1)(e^a+ae^a)

expand

ln (a + 1) \cdot (e^{a} + a \cdot e^{a})

e^{a} ln (a + 1) + a e^{a} ln (a + 1)

Solution steps

ln (a + 1) (e^{a} + a e^{a})

Apply the distributive law:

a (b + c) = ab + a c

a = ln (a + 1), b = e^{a}, c = a e^{a}

= ln (a + 1) e^{a} + ln (a + 1) a e^{a}

= e^{a} ln (a + 1) + a e^{a} ln (a + 1)

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(2 x y - sec^{2} (x)) d x + (x^{2} + 2 y) d y

What is expand ln(a+1)*(e^a+a*e^a) ?
The solution to expand ln(a+1)*(e^a+a*e^a) is e^aln(a+1)+ae^aln(a+1)