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(ax^(n))/(x^(n+1)+b)

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(d^(n))/(dx^(n))((1)/(ax+b))

(d^(n))/(dx^(n))(log x)=(a)((n-1)!)/(x^(n))(b)(n!)/(x^(n))(c)((n-2)!)/(x^(n))(d)(-1)^(n-1)((n-1)!)/(x^(n))

(d^n)/(dx^n)(logx)=? (a) ((n-1)!)/(x^n) (b) (n !)/(x^n) (c) ((n-2)!)/(x^n) (d) (-1)^(n-1)((n-1)!)/(x^n)

By substitution: Theorem: int (ax+b)^n dx = (ax+b)^(n+1)/(a(n+1))

By substitution: Theorem: int (ax+b)^n dx = (ax+b)^(n+1)/(a(n+1))

lim_(x rarr a)x^(n) + ax^(n-1) +a^(2)x^(n-2) + .........+a^(n)= ________.

(ax)^(m)+(b)^(n)

By substitution: Theorem: If int(ax+b)^(n)dx=((ax+b)^(n+1))/(a)(n+1)

If I_(n) = int x^(-n) e^(ax) dx then prove that I_(n)=(-e^(ax))/((n-1)x^(n-1))+(a)/(n-1)I_(n-1)