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Popular Calculus Problems

integral of (ln(x))/(x(1+ln^2(x)))	\int\:\frac{\ln(x)}{x(1+\ln^{2}(x))}dx
integral from 0 to 15 of 1000e^{-0.05x}	\int\:_{0}^{15}1000e^{-0.05x}dx
derivative of (5x^2-2(x^3+3x))	\frac{d}{dx}((5x^{2}-2)(x^{3}+3x))
derivative of 3x\sqrt[4]{x^4-2}	\frac{d}{dx}(3x\sqrt[4]{x^{4}-2})
derivative of 4x^3+2+1/x	\frac{d}{dx}(4x^{3}+2+\frac{1}{x})
(dy)/(dx)=2xe^{5y}	\frac{dy}{dx}=2xe^{5y}
(\partial)/(\partial x)(xsin(2x))	\frac{\partial\:}{\partial\:x}(x\sin(2x))
derivative of 21x^3+9/x	\frac{d}{dx}(21x^{3}+\frac{9}{x})
(\partial)/(\partial x)(xe^{x/y})	\frac{\partial\:}{\partial\:x}(xe^{\frac{x}{y}})
slope of (6,-12),(10,-8)	slope\:(6,-12),(10,-8)
integral of (x^2+2x)/(sqrt(x^3+3x^2+1))	\int\:\frac{x^{2}+2x}{\sqrt{x^{3}+3x^{2}+1}}dx
integral of 1/(\sqrt[3]{x)+sqrt(x)}	\int\:\frac{1}{\sqrt[3]{x}+\sqrt{x}}dx
integral of (((ln(x))^3))/x	\int\:\frac{((\ln(x))^{3})}{x}dx
derivative of f(x)=2x^{1/2}	derivative\:f(x)=2x^{\frac{1}{2}}
integral of 3sin^2(x)cos^4(x)	\int\:3\sin^{2}(x)\cos^{4}(x)dx
integral from 0 to 3 of (x-1)(x-2)(x-3)	\int\:_{0}^{3}(x-1)(x-2)(x-3)dx
slope ofintercept (-7,-9),(0,-7)	slopeintercept\:(-7,-9),(0,-7)
integral of (4-y^2)^{1/2}	\int\:(4-y^{2})^{\frac{1}{2}}dy
derivative of sin(1-xcos^3(x))	\frac{d}{dx}(\sin(1-x)\cos^{3}(x))
derivative of f(x)=(e^x)/(2+5x)	derivative\:f(x)=\frac{e^{x}}{2+5x}
sqrt(x)+(sqrt(y)dy)/(dx)=0	\sqrt{x}+\frac{\sqrt{y}dy}{dx}=0
6y^'-2y=xy^4,y(0)=-2	6y^{\prime\:}-2y=xy^{4},y(0)=-2
derivative of f(x)=(6x+16)/(x+3)	derivative\:f(x)=\frac{6x+16}{x+3}
derivative of xsqrt(x)+x^2sqrt(x)	\frac{d}{dx}(x\sqrt{x}+x^{2}\sqrt{x})
integral of (w^2+z^2)^{(-1)/2}w	\int\:(w^{2}+z^{2})^{\frac{-1}{2}}wdw
derivative of 4e^{4x}cos(5x)	derivative\:4e^{4x}\cos(5x)
y^{''}+9y=2sin(2t),y(0)=0,y^'(0)=-1	y^{\prime\:\prime\:}+9y=2\sin(2t),y(0)=0,y^{\prime\:}(0)=-1
taylor 1/(1-x-x^2),0	taylor\:\frac{1}{1-x-x^{2}},0
sum from n=0 to infinity of 4546644	\sum\:_{n=0}^{\infty\:}4546644
limit as x approaches 3 of (x^x+x)^x	\lim\:_{x\to\:3}((x^{x}+x)^{x})
(ln(x/3))^'	(\ln(\frac{x}{3}))^{\prime\:}
derivative of x^3(x-7)^2	derivative\:x^{3}(x-7)^{2}
tangent of y=x^2+3	tangent\:y=x^{2}+3
(\partial)/(\partial y)(sqrt(41-x^2-4y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{41-x^{2}-4y^{2}})
y^{''}+y/a =0	y^{\prime\:\prime\:}+\frac{y}{a}=0
integral of 1/(x^3+x^2+x+1)	\int\:\frac{1}{x^{3}+x^{2}+x+1}dx
integral from 0 to 1 of pi(x^2-x^4)	\int\:_{0}^{1}π(x^{2}-x^{4})dx
(\partial)/(\partial x)(y*arcsin(x/y))	\frac{\partial\:}{\partial\:x}(y\cdot\:\arcsin(\frac{x}{y}))
derivative of sqrt(6t^2-t)	derivative\:\sqrt{6t^{2}-t}
derivative of f(x)=x^2tan(x)	derivative\:f(x)=x^{2}\tan(x)
integral of 1/(x^2+x-1)	\int\:\frac{1}{x^{2}+x-1}dx
integral from 1 to 4 of 4/(x^2+4x+4)	\int\:_{1}^{4}\frac{4}{x^{2}+4x+4}dx
limit as x approaches 0 of-2	\lim\:_{x\to\:0}(-2)
derivative of 8cos(3x)	\frac{d}{dx}(8\cos(3x))
integral of xIn(x)	\int\:xIn(x)dx
derivative of (2000x/(4x+75))	\frac{d}{dx}(\frac{2000x}{4x+75})
f(x)=6xarcsin(x)	f(x)=6x\arcsin(x)
integral of 5tan^2(y)	\int\:5\tan^{2}(y)dy
integral of sin^2((5x)/2)	\int\:\sin^{2}(\frac{5x}{2})dx
(2x+1)y^'+2y=4x	(2x+1)y^{\prime\:}+2y=4x
derivative of 1-sec^2(x)	\frac{d}{dx}(1-\sec^{2}(x))
integral of 1/(5y)	\int\:\frac{1}{5y}dy
y^{''}+y=0,y(pi/3)=0,y^'(pi/3)=8	y^{\prime\:\prime\:}+y=0,y(\frac{π}{3})=0,y^{\prime\:}(\frac{π}{3})=8
(\partial)/(\partial x)(3x+9x^{17})	\frac{\partial\:}{\partial\:x}(3x+9x^{17})
integral of \sqrt[4]{x^3}+1	\int\:\sqrt[4]{x^{3}}+1dx
limit as x approaches 0-of x^3cos(2/x)	\lim\:_{x\to\:0-}(x^{3}\cos(\frac{2}{x}))
derivative of (e^x/(4x^3))	\frac{d}{dx}(\frac{e^{x}}{4x^{3}})
integral of 1/(1-tan(x))	\int\:\frac{1}{1-\tan(x)}dx
derivative of (-x^2-9/((x^2-9)^2))	\frac{d}{dx}(\frac{-x^{2}-9}{(x^{2}-9)^{2}})
derivative of (x^2/(5+4x))	\frac{d}{dx}(\frac{x^{2}}{5+4x})
(x^2+1)y^'+4x(y-1)=0,y(0)=5	(x^{2}+1)y^{\prime\:}+4x(y-1)=0,y(0)=5
integral of xsqrt(16-25x^2)	\int\:x\sqrt{16-25x^{2}}dx
integral from 0 to pi/2 of 3cos(x)	\int\:_{0}^{\frac{π}{2}}3\cos(x)dx
derivative of f(x)=(3x^3+2x)(x-2)(x+4)	derivative\:f(x)=(3x^{3}+2x)(x-2)(x+4)
integral of 1/((4x^2-25)^{3/2)}	\int\:\frac{1}{(4x^{2}-25)^{\frac{3}{2}}}dx
integral of sqrt(-4x^2-12x-5)	\int\:\sqrt{-4x^{2}-12x-5}dx
limit as x approaches 0+of 2/(sqrt(x))	\lim\:_{x\to\:0+}(\frac{2}{\sqrt{x}})
integral of 1/(x^pi)	\int\:\frac{1}{x^{π}}dx
limit as x approaches 0 of (6x)/(3x)	\lim\:_{x\to\:0}(\frac{6x}{3x})
(dy)/(dx)=e^{9x-6y}	\frac{dy}{dx}=e^{9x-6y}
derivative of (ln(x)/(x+1))	\frac{d}{dx}(\frac{\ln(x)}{x+1})
sum from k=1 to infinity of sin(kpi)	\sum\:_{k=1}^{\infty\:}\sin(kπ)
integral of (4x-11)/((2x-1)(x+4))	\int\:\frac{4x-11}{(2x-1)(x+4)}dx
derivative of 6x^2+5x-6	\frac{d}{dx}(6x^{2}+5x-6)
integral of 1/4 x	\int\:\frac{1}{4}xdx
inverse oflaplace ((6s+3))/(s^2)	inverselaplace\:\frac{(6s+3)}{s^{2}}
derivative of ((1+x/(1-x))^2)	\frac{d}{dx}((\frac{1+x}{1-x})^{2})
(d^4)/(dx^4)(1/(3x+1))	\frac{d^{4}}{dx^{4}}(\frac{1}{3x+1})
integral of 2x^3+4x+5	\int\:2x^{3}+4x+5dx
limit as x approaches pi of sin(11/6)	\lim\:_{x\to\:π}(\sin(\frac{11}{6}))
derivative of 1/8 x^4-(32)/(x^3)	derivative\:\frac{1}{8}x^{4}-\frac{32}{x^{3}}
integral from-4pi to 4pi of (sin^2(x)+1)	\int\:_{-4π}^{4π}(\sin^{2}(x)+1)dx
area x^3-11x^2+28x,-x^3+11x^2-28x	area\:x^{3}-11x^{2}+28x,-x^{3}+11x^{2}-28x
limit as x approaches infinity of 6x-1	\lim\:_{x\to\:\infty\:}(6x-1)
y^'=e^{x^2}	y^{\prime\:}=e^{x^{2}}
derivative of e^{ln(ln(2x)})	\frac{d}{dx}(e^{\ln(\ln(2x))})
derivative of (3x)/(2e^x-e^{-x)}	derivative\:\frac{3x}{2e^{x}-e^{-x}}
limit as x approaches 2 of 4/((x-2)^2)	\lim\:_{x\to\:2}(\frac{4}{(x-2)^{2}})
derivative of f(x)=322560(2x+5)	derivative\:f(x)=322560(2x+5)
(dy)/(dx)=sin(5x),y(0)=2	\frac{dy}{dx}=\sin(5x),y(0)=2
(d^3)/(dx^3)(sqrt(x+1))	\frac{d^{3}}{dx^{3}}(\sqrt{x+1})
sum from n=0 to infinity of (n!)/(5^n)	\sum\:_{n=0}^{\infty\:}\frac{n!}{5^{n}}
slope ofintercept (4,-7),(2,-1)	slopeintercept\:(4,-7),(2,-1)
derivative of 8ysin(x)	\frac{d}{dx}(8y\sin(x))
taylor cos(x),pi	taylor\:\cos(x),π
integral of 8x^3(2x^4+4)	\int\:8x^{3}(2x^{4}+4)dx
derivative of cos(x-1/2)	\frac{d}{dx}(\cos(x)-\frac{1}{2})
integral from 0 to 1 of xe^{3x}	\int\:_{0}^{1}xe^{3x}dx
integral of 9x(1-x)	\int\:9x(1-x)dx
integral from 0 to pi of-cos(x)	\int\:_{0}^{π}-\cos(x)dx

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