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Popular Calculus Problems

integral of 50x^3sqrt(1-25x^2)	\int\:50x^{3}\sqrt{1-25x^{2}}dx
derivative of (3-5xe^x(3x+2))	\frac{d}{dx}((3-5xe^{x})(3x+2))
limit as x approaches-2 of (-3)/(2-x)	\lim\:_{x\to\:-2}(\frac{-3}{2-x})
(\partial)/(\partial x)(log_{5}(x))	\frac{\partial\:}{\partial\:x}(\log_{5}(x))
derivative of ln(sqrt((2x+1)/(x^2-3)))	derivative\:\ln(\sqrt{\frac{2x+1}{x^{2}-3}})
derivative of g(x)=sqrt(5-x)	derivative\:g(x)=\sqrt{5-x}
integral of 1/2 x^2ln(x)-1/2 x^2ln(2x)	\int\:\frac{1}{2}x^{2}\ln(x)-\frac{1}{2}x^{2}\ln(2x)dx
integral of ln(-x)	\int\:\ln(-x)dx
limit as x approaches 0+of ln(x)x	\lim\:_{x\to\:0+}(\ln(x)x)
integral of (x/(1-x^2))	\int\:(\frac{x}{1-x^{2}})dx
derivative of sec(x-1)	\frac{d}{dx}(\sec(x)-1)
integral of 2/(x^2+2)	\int\:\frac{2}{x^{2}+2}dx
f(x)=cos(x)e^x	f(x)=\cos(x)e^{x}
integral of x/(1+x^3)	\int\:\frac{x}{1+x^{3}}dx
derivative of 3+3cos(x^3-4sin(x^3))	\frac{d}{dx}(3+3\cos(x^{3})-4\sin(x^{3}))
integral from 3 to 5 of ln(x^2+1)	\int\:_{3}^{5}\ln(x^{2}+1)dx
derivative of arctan(sqrt(x/a))	\frac{d}{dx}(\arctan(\sqrt{\frac{x}{a}}))
derivative of-1/2 e^{-x/2}	\frac{d}{dx}(-\frac{1}{2}e^{-\frac{x}{2}})
integral of (x^2-3x+11)/((x^2-4x+10)^2)	\int\:\frac{x^{2}-3x+11}{(x^{2}-4x+10)^{2}}dx
derivative of f(x)=(x^3)/(4-x^2)	derivative\:f(x)=\frac{x^{3}}{4-x^{2}}
integral of sqrt(1+u^2)	\int\:\sqrt{1+u^{2}}du
integral from 0 to 4 of x^3sqrt(x^2+16)	\int\:_{0}^{4}x^{3}\sqrt{x^{2}+16}dx
derivative of 3x^2+2x+1	\frac{d}{dx}(3x^{2}+2x+1)
t^2y^'+ty=5	t^{2}y^{\prime\:}+ty=5
laplacetransform xsin(3x)	laplacetransform\:x\sin(3x)
derivative of 1/(e^x+1)	\frac{d}{dx}(\frac{1}{e^{x}+1})
taylor x*ln(x)	taylor\:x\cdot\:\ln(x)
integral of (x+1)/(x^3)	\int\:\frac{x+1}{x^{3}}dx
derivative of xe^{8x}	\frac{d}{dx}(xe^{8x})
sum from n=0 to infinity of 4^{2n+1}	\sum\:_{n=0}^{\infty\:}4^{2n+1}
(\partial)/(\partial x)(\|x-y\|)	\frac{\partial\:}{\partial\:x}(\left\|x-y\right\|)
derivative of ln^4(((x^2-1^3)/(x^2-1)))	\frac{d}{dx}(\ln^{4}(\frac{(x^{2}-1)^{3}}{x^{2}-1}))
integral of sin(x)sin(cos(x))	\int\:\sin(x)\sin(\cos(x))dx
tangent of f(x)=5-x^2,\at x=-1	tangent\:f(x)=5-x^{2},\at\:x=-1
integral of 1/(x^6-x^3)	\int\:\frac{1}{x^{6}-x^{3}}dx
integral of (4x^3+cos(x))	\int\:(4x^{3}+\cos(x))dx
y^'=(x^2-y^2)/(xy)	y^{\prime\:}=\frac{x^{2}-y^{2}}{xy}
derivative of 2/(sqrt(u))	derivative\:\frac{2}{\sqrt{u}}
integral of (x^2-9x+3)	\int\:(x^{2}-9x+3)dx
(\partial)/(\partial x)(xy+ln(x/y))	\frac{\partial\:}{\partial\:x}(xy+\ln(\frac{x}{y}))
integral of (-16x+3)/((x^2+2)^2)	\int\:\frac{-16x+3}{(x^{2}+2)^{2}}dx
(\partial)/(\partial x)(e^{(3x+4y)}cos(5z))	\frac{\partial\:}{\partial\:x}(e^{(3x+4y)}\cos(5z))
(\partial)/(\partial y)(4+x^3+y^3-3xy)	\frac{\partial\:}{\partial\:y}(4+x^{3}+y^{3}-3xy)
derivative of (x^2-9x+20/((x-2)(x+2)))	\frac{d}{dx}(\frac{x^{2}-9x+20}{(x-2)(x+2)})
integral of sinh(6x)	\int\:\sinh(6x)dx
integral of (sin(x))/(1-cos(x))	\int\:\frac{\sin(x)}{1-\cos(x)}dx
integral of 2csc(x)	\int\:2\csc(x)dx
derivative of bcos(x+x^2sin(x))	\frac{d}{dx}(b\cos(x)+x^{2}\sin(x))
limit as y approaches-1 of y^3-2y^2+3y-4	\lim\:_{y\to\:-1}(y^{3}-2y^{2}+3y-4)
laplacetransform 1/2+1/2 cos(2t)	laplacetransform\:\frac{1}{2}+\frac{1}{2}\cos(2t)
integral from 0 to 4 of 4/(2x+1)	\int\:_{0}^{4}\frac{4}{2x+1}dx
integral of 1/(\sqrt[3]{x)+1}	\int\:\frac{1}{\sqrt[3]{x}+1}dx
(\partial)/(\partial y)(e^{2xy}cos(x))	\frac{\partial\:}{\partial\:y}(e^{2xy}\cos(x))
integral of 2t^2	\int\:2t^{2}dt
laplacetransform cos(3t+5)e^{2t}	laplacetransform\:\cos(3t+5)e^{2t}
integral of 1/(1-x^2)ln((1+x)/(1-x))	\int\:\frac{1}{1-x^{2}}\ln(\frac{1+x}{1-x})dx
integral from 0 to pi/3 of sin(x)	\int\:_{0}^{\frac{π}{3}}\sin(x)dx
derivative of y=ln(x+sqrt(x^2+9))	derivative\:y=\ln(x+\sqrt{x^{2}+9})
derivative of 3(sin(x+xcos(x)))	\frac{d}{dx}(3(\sin(x)+x\cos(x)))
sum from n=1 to infinity of 2^{1/n}	\sum\:_{n=1}^{\infty\:}2^{\frac{1}{n}}
(\partial)/(\partial x)(3x^2+2xy)	\frac{\partial\:}{\partial\:x}(3x^{2}+2xy)
integral of 1/(4^x)	\int\:\frac{1}{4^{x}}dx
integral of xe^{-6x^2}	\int\:xe^{-6x^{2}}dx
limit as x approaches-2 of 4x^2-3x+5	\lim\:_{x\to\:-2}(4x^{2}-3x+5)
(sqrt(y^2+1))/(ydy)= x/(dx)	\frac{\sqrt{y^{2}+1}}{ydy}=\frac{x}{dx}
derivative of 2x^2-4x+5	\frac{d}{dx}(2x^{2}-4x+5)
derivative of e^x(2x^4+3cos(x))	\frac{d}{dx}(e^{x}(2x^{4}+3\cos(x)))
derivative of-2x^3+8/(x^2-6x-1)	\frac{d}{dx}(-2x^{3}+\frac{8}{x^{2}}-6x-1)
integral of-8x^3cos(5x^4+1)	\int\:-8x^{3}\cos(5x^{4}+1)dx
derivative of 3e^{6x}	derivative\:3e^{6x}
(\partial)/(\partial x)(16x-4y-6yx)	\frac{\partial\:}{\partial\:x}(16x-4y-6yx)
integral from-1 to 2 of (2-5x+1/2 x^2)	\int\:_{-1}^{2}(2-5x+\frac{1}{2}x^{2})dx
f(x)=(x+9)^{1/2}	f(x)=(x+9)^{\frac{1}{2}}
derivative of f(x)=-x^2-x	derivative\:f(x)=-x^{2}-x
derivative of (ln(8)^x)	\frac{d}{dx}((\ln(8))^{x})
(\partial)/(\partial x)(sin^6(3x-4y))	\frac{\partial\:}{\partial\:x}(\sin^{6}(3x-4y))
d/(dy)((4-y)^{1/3})	\frac{d}{dy}((4-y)^{\frac{1}{3}})
limit as x approaches 0 of 3x+5	\lim\:_{x\to\:0}(3x+5)
y^'-6/x y=(y^5)/(x^{20)},y(1)=1	y^{\prime\:}-\frac{6}{x}y=\frac{y^{5}}{x^{20}},y(1)=1
slope of-3x^4+11x^2	slope\:-3x^{4}+11x^{2}
integral of cos^4(7x)	\int\:\cos^{4}(7x)dx
(\partial)/(\partial y)((1+x^2)/(3y-y^2))	\frac{\partial\:}{\partial\:y}(\frac{1+x^{2}}{3y-y^{2}})
d/(dj)(2i+3j)	\frac{d}{dj}(2i+3j)
derivative of x^2-4	derivative\:x^{2}-4
(x^2+1)^'	(x^{2}+1)^{\prime\:}
integral of (e^{x+2})/(e^{x+1)}	\int\:\frac{e^{x+2}}{e^{x+1}}dx
derivative of 18cos(θ)+9sin^2(θ)	derivative\:18\cos(θ)+9\sin^{2}(θ)
(d^2)/(dx^2)(5e^{-x^2})	\frac{d^{2}}{dx^{2}}(5e^{-x^{2}})
derivative of 1/(sqrt(x)+1/(sqrt(y)))	\frac{d}{dx}(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{y}})
tangent of f(x)=5e^x+x,\at x=0	tangent\:f(x)=5e^{x}+x,\at\:x=0
derivative of (-e^{-x/2}x+e^{-x/2}/2)	\frac{d}{dx}(\frac{-e^{-\frac{x}{2}}x+e^{-\frac{x}{2}}}{2})
(dy)/(dx)=-7e^{x+y}	\frac{dy}{dx}=-7e^{x+y}
integral of cos(x)x	\int\:\cos(x)xdx
derivative of f(x)= 1/(3x)	derivative\:f(x)=\frac{1}{3x}
derivative of f(x)=sqrt(2x^3-4x-8x+6)	derivative\:f(x)=\sqrt{2x^{3}-4x-8x+6}
sum from n=0 to infinity of 1/(e^{n^2)}	\sum\:_{n=0}^{\infty\:}\frac{1}{e^{n^{2}}}
integral from 0 to 4 of e^xsin(x)	\int\:_{0}^{4}e^{x}\sin(x)dx
(\partial)/(\partial x)(x^2+3y^3)	\frac{\partial\:}{\partial\:x}(x^{2}+3y^{3})
integral of (100)/(w^2sqrt(25-w^2))	\int\:\frac{100}{w^{2}\sqrt{25-w^{2}}}dw
xy^'-2y=3x^2	xy^{\prime\:}-2y=3x^{2}

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