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Popular Calculus Problems

derivative of log_{3}(2x)	\frac{d}{dx}(\log_{3}(2x))
taylor (1+x)^{-3}	taylor\:(1+x)^{-3}
integral of x/(sqrt(x^2+x+2))	\int\:\frac{x}{\sqrt{x^{2}+x+2}}dx
integral of (12x^2-8x+5)	\int\:(12x^{2}-8x+5)dx
integral of 7t	\int\:7tdt
(\partial)/(\partial y)(x^2-xy+5y^2)	\frac{\partial\:}{\partial\:y}(x^{2}-xy+5y^{2})
integral of sin(7pit)	\int\:\sin(7πt)dt
derivative of x^3arctan(5x)	\frac{d}{dx}(x^{3}\arctan(5x))
integral of (9(1-tan^2(x)))/(sec^2(x))	\int\:\frac{9(1-\tan^{2}(x))}{\sec^{2}(x)}dx
derivative of csc(x+cot(x))	\frac{d}{dx}(\csc(x)+\cot(x))
derivative of (ln(x))/(5x^3)	derivative\:\frac{\ln(x)}{5x^{3}}
(4x^3y^2-6x^2y-2x-3)dx+(2x^4y-2x^3)dy=0	(4x^{3}y^{2}-6x^{2}y-2x-3)dx+(2x^{4}y-2x^{3})dy=0
laplacetransform e^{-t}sin(3t)	laplacetransform\:e^{-t}\sin(3t)
((2y)/x+2x)+((2ln(x)-3)dy)/(dx)=0	(\frac{2y}{x}+2x)+\frac{(2\ln(x)-3)dy}{dx}=0
sum from n=0 to infinity of n^2(1/2)^n	\sum\:_{n=0}^{\infty\:}n^{2}(\frac{1}{2})^{n}
limit as x approaches 0 of (1/x)^{tan(x)}	\lim\:_{x\to\:0}((\frac{1}{x})^{\tan(x)})
derivative of cos(x-x^2(1-2x))	\frac{d}{dx}(\cos(x-x^{2})(1-2x))
limit as x approaches 0 of x^{13x}	\lim\:_{x\to\:0}(x^{13x})
limit as x approaches 0 of 1/x ln(1-2x)	\lim\:_{x\to\:0}(\frac{1}{x}\ln(1-2x))
y^'=y^{(5/3)}	y^{\prime\:}=y^{(\frac{5}{3})}
derivative of (2x+3x^2/(x^2e^x))	\frac{d}{dx}(\frac{2x+3x^{2}}{x^{2}e^{x}})
(\partial)/(\partial x)(cos(x+y^3))	\frac{\partial\:}{\partial\:x}(\cos(x+y^{3}))
laplacetransform te^{-3t}cos(3t)	laplacetransform\:te^{-3t}\cos(3t)
derivative of (80-x/4)	\frac{d}{dx}(\frac{80-x}{4})
integral of (7x^3-x^2+8x+12)/(x^4+4x^2)	\int\:\frac{7x^{3}-x^{2}+8x+12}{x^{4}+4x^{2}}dx
(\partial)/(\partial y)(x^2+y/x)	\frac{\partial\:}{\partial\:y}(x^{2}+\frac{y}{x})
derivative of sin^2(x^3+4x^2-3)	\frac{d}{dx}(\sin^{2}(x^{3}+4x^{2}-3))
limit as x approaches 0-of (x^2-x)/(x-1)	\lim\:_{x\to\:0-}(\frac{x^{2}-x}{x-1})
integral from 0 to 2 of 5x^9	\int\:_{0}^{2}5x^{9}dx
integral of 2e^{2x}+12x^3+4x	\int\:2e^{2x}+12x^{3}+4xdx
derivative of-sqrt(2x^2+y^2)	\frac{d}{dx}(-\sqrt{2x^{2}+y^{2}})
derivative of In(x+1/(sqrt(x-1)))	\frac{d}{dx}(In\frac{x+1}{\sqrt{x-1}})
integral of xsin^2(2x)	\int\:x\sin^{2}(2x)dx
derivative of (x^2+3xe^{2x})	\frac{d}{dx}((x^{2}+3x)e^{2x})
derivative of 4t^3	derivative\:4t^{3}
limit as x approaches infinity+of 4x	\lim\:_{x\to\:\infty\:+}(4x)
derivative of [x+(x+sin^2(x))^3]^6	derivative\:[x+(x+\sin^{2}(x))^{3}]^{6}
integral of xe^{yx}	\int\:xe^{yx}dx
integral of (ln(x))/(x(1-ln^2(x)))	\int\:\frac{\ln(x)}{x(1-\ln^{2}(x))}dx
integral from-1 to 5 of \|x-2\|	\int\:_{-1}^{5}\left\|x-2\right\|dx
integral from 0 to pi/2 of-9sin^2(3x)	\int\:_{0}^{\frac{π}{2}}-9\sin^{2}(3x)dx
laplacetransform 7cos(3t)	laplacetransform\:7\cos(3t)
integral of (2+x^5)^8x^4	\int\:(2+x^{5})^{8}x^{4}dx
d/(ds)(s/(s^2+w^2))	\frac{d}{ds}(\frac{s}{s^{2}+w^{2}})
derivative of-8e^{-3x}	\frac{d}{dx}(-8e^{-3x})
derivative of-18cos(3x)	\frac{d}{dx}(-18\cos(3x))
integral of (sin^5(θ))/(sqrt(cos(θ)))	\int\:\frac{\sin^{5}(θ)}{\sqrt{\cos(θ)}}dθ
derivative of f(x)=(3x^3+3x)(x-3)(x+5)	derivative\:f(x)=(3x^{3}+3x)(x-3)(x+5)
derivative of e^xx^4+8e^xx^3+12e^xx^2	derivative\:e^{x}x^{4}+8e^{x}x^{3}+12e^{x}x^{2}
(dy)/(dx)=1-y+x^2-yx^2	\frac{dy}{dx}=1-y+x^{2}-yx^{2}
integral from 0 to 1 of (x^2+1)e^{-x}	\int\:_{0}^{1}(x^{2}+1)e^{-x}dx
sum from n=0 to infinity of 2/(5^n)	\sum\:_{n=0}^{\infty\:}\frac{2}{5^{n}}
derivative of sqrt(csc(2x))	\frac{d}{dx}(\sqrt{\csc(2x)})
(dy)/(dx)=-(sqrt(x))/(4y)	\frac{dy}{dx}=-\frac{\sqrt{x}}{4y}
(\partial)/(\partial y)(8xy^2z^3)	\frac{\partial\:}{\partial\:y}(8xy^{2}z^{3})
integral from 0 to 2 of sin(x)	\int\:_{0}^{2}\sin(x)dx
integral of (-5x+2)/((x+1)^2)	\int\:\frac{-5x+2}{(x+1)^{2}}dx
derivative of cos(x-pi/6)	\frac{d}{dx}(\cos(x-\frac{π}{6}))
y^'=ye^x	y^{\prime\:}=ye^{x}
derivative of y=(1-5x)^6	derivative\:y=(1-5x)^{6}
tangent of y=sqrt(7x+1),(5,6)	tangent\:y=\sqrt{7x+1},(5,6)
limit as x approaches 0 of (1+3x)^{4/x}	\lim\:_{x\to\:0}((1+3x)^{\frac{4}{x}})
(\partial)/(\partial x)((y-x^2)(2y^2+x))	\frac{\partial\:}{\partial\:x}((y-x^{2})(2y^{2}+x))
integral of 5/(36+x^2)	\int\:\frac{5}{36+x^{2}}dx
(\partial)/(\partial y)(xy(1-x-y))	\frac{\partial\:}{\partial\:y}(xy(1-x-y))
derivative of y=x^4+2e^x	derivative\:y=x^{4}+2e^{x}
limit as x approaches 9 of \|x+3\|	\lim\:_{x\to\:9}(\left\|x+3\right\|)
3t*(dy)/(dt)-y=sqrt(t)	3t\cdot\:\frac{dy}{dt}-y=\sqrt{t}
integral of x+e^{4x}	\int\:x+e^{4x}dx
(\partial)/(\partial x)(3ax^2+e^xx+e^x)	\frac{\partial\:}{\partial\:x}(3ax^{2}+e^{x}x+e^{x})
integral from-1 to 4 of (7y)/(y^2-3y-10)	\int\:_{-1}^{4}\frac{7y}{y^{2}-3y-10}dy
limit as x approaches pi/2+of sin(x)	\lim\:_{x\to\:\frac{π}{2}+}(\sin(x))
derivative of (3x^2-9^{-14})	\frac{d}{dx}((3x^{2}-9)^{-14})
tangent of y=x^2-7x+7,(0,7)	tangent\:y=x^{2}-7x+7,(0,7)
integral of 1/(sqrt(x))cos^2(sqrt(x))	\int\:\frac{1}{\sqrt{x}}\cos^{2}(\sqrt{x})dx
integral from 0 to a of 7x^2sqrt(a^2-x^2)	\int\:_{0}^{a}7x^{2}\sqrt{a^{2}-x^{2}}dx
derivative of sqrt(4x^2-8x)	\frac{d}{dx}(\sqrt{4x^{2}-8x})
integral of (x^2)/((1+x^3)^{1.7)}	\int\:\frac{x^{2}}{(1+x^{3})^{1.7}}dx
slope of (38)(3-4)	slope\:(38)(3-4)
limit as x approaches 16 of (sqrt(x-4))/(\sqrt[4]{x-2)}	\lim\:_{x\to\:16}(\frac{\sqrt{x-4}}{\sqrt[4]{x-2}})
limit as x approaches infinity of e^{-3x}sin(x)	\lim\:_{x\to\:\infty\:}(e^{-3x}\sin(x))
integral from-1 to 1 of (x^2-x^4)	\int\:_{-1}^{1}(x^{2}-x^{4})dx
derivative of-4sin(x)-9ln(x)+11	derivative\:-4\sin(x)-9\ln(x)+11
y^{''}+k^2y=cos(kx)	y^{\prime\:\prime\:}+k^{2}y=\cos(kx)
integral from 0 to 2 of (12)/(x^2+4)	\int\:_{0}^{2}\frac{12}{x^{2}+4}dx
(\partial)/(\partial y)(y-x^2)	\frac{\partial\:}{\partial\:y}(y-x^{2})
integral of 3^3	\int\:3^{3}
integral of (1/x-1)^2	\int\:(\frac{1}{x}-1)^{2}dx
derivative of f(x)=cos((x+1)/(x-1))	derivative\:f(x)=\cos(\frac{x+1}{x-1})
(\partial)/(\partial x)(3x^2y-y^3+x-y)	\frac{\partial\:}{\partial\:x}(3x^{2}y-y^{3}+x-y)
limit as x approaches 0 of x^3cos(2/x)	\lim\:_{x\to\:0}(x^{3}\cos(\frac{2}{x}))
integral of (30)/((x-1)(x^2+9))	\int\:\frac{30}{(x-1)(x^{2}+9)}dx
derivative of f(x)=(4x^3)/(x^4+1)	derivative\:f(x)=\frac{4x^{3}}{x^{4}+1}
d/(d{z)}(ln(sqrt({x)^2+{y}^2+{z}^2}))	\frac{d}{d{z}}(\ln(\sqrt{{x}^{2}+{y}^{2}+{z}^{2}}))
integral of 1/(2x^2+1)	\int\:\frac{1}{2x^{2}+1}dx
integral from 3pi to 4pi of 2sin(x)	\int\:_{3π}^{4π}2\sin(x)dx
integral of 1/(xsqrt(9x^2-16))	\int\:\frac{1}{x\sqrt{9x^{2}-16}}dx
(\partial)/(\partial y)(2x^2+y^2)	\frac{\partial\:}{\partial\:y}(2x^{2}+y^{2})
x^2(dy)/(dx)=xy+x^2e^{y/x}	x^{2}\frac{dy}{dx}=xy+x^{2}e^{\frac{y}{x}}
y^{''}+6y+8=0,y(0)=0,y^'(0)=12	y^{\prime\:\prime\:}+6y+8=0,y(0)=0,y^{\prime\:}(0)=12

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