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Popular Calculus Problems

integral from 60 to v of 1/(-0.4v^3)	\int\:_{60}^{v}\frac{1}{-0.4v^{3}}dv
inverse oflaplace ((5/s-1))/((s+1)^2+9)	inverselaplace\:\frac{(\frac{5}{s}-1)}{(s+1)^{2}+9}
integral of 1/(sqrt(1+6x-3x^2))	\int\:\frac{1}{\sqrt{1+6x-3x^{2}}}dx
y^'-2y=3e^{-2t}	y^{\prime\:}-2y=3e^{-2t}
derivative of (e^{x^2}/2)	\frac{d}{dx}(\frac{e^{x^{2}}}{2})
(x+1)(dy)/(dx)+(x+2)y=6xe^{-x}	(x+1)\frac{dy}{dx}+(x+2)y=6xe^{-x}
derivative of log_{10}(n)	derivative\:\log_{10}(n)
integral from 0 to 1/2 of arcsin(2x)	\int\:_{0}^{\frac{1}{2}}\arcsin(2x)dx
integral of (4x+1)/((2x^2+x)^5)	\int\:\frac{4x+1}{(2x^{2}+x)^{5}}dx
(\partial)/(\partial x)(8x^2+14xy+5y^2)	\frac{\partial\:}{\partial\:x}(8x^{2}+14xy+5y^{2})
tangent of x^2+y^2=25,(4,3)	tangent\:x^{2}+y^{2}=25,(4,3)
integral of-2/(x^2+1)	\int\:-\frac{2}{x^{2}+1}dx
(\partial)/(\partial x)(5e^{xy+4})	\frac{\partial\:}{\partial\:x}(5e^{xy+4})
y^{''}+25y=2tan(5x)	y^{\prime\:\prime\:}+25y=2\tan(5x)
inverse oflaplace (2s+5)/(s^2+5s+6)	inverselaplace\:\frac{2s+5}{s^{2}+5s+6}
derivative of arctan({g}(x)x)	\frac{d}{dx}(\arctan({g}(x))x)
taylor sqrt(x),x=1	taylor\:\sqrt{x},x=1
tangent of y=3x^3+x^2-8x+4,(-2,0)	tangent\:y=3x^{3}+x^{2}-8x+4,(-2,0)
integral of (3x)/(sqrt(7-x^2))	\int\:\frac{3x}{\sqrt{7-x^{2}}}dx
derivative of-(4x/((x^2+4)^2))	\frac{d}{dx}(-\frac{4x}{(x^{2}+4)^{2}})
integral of sin(θ)+cos(θ)	\int\:\sin(θ)+\cos(θ)dθ
limit as x approaches 5 of 4	\lim\:_{x\to\:5}(4)
parity x^{8cos(x)}	parity\:x^{8\cos(x)}
xy^'+(1+6x)y=24e^{-6x}	xy^{\prime\:}+(1+6x)y=24e^{-6x}
integral of 1/(4x+7)	\int\:\frac{1}{4x+7}dx
integral of (8arcsin(x))/(x^2)	\int\:\frac{8\arcsin(x)}{x^{2}}dx
derivative of (sqrt(x)+4x)(x^{3/2}-x)	derivative\:(\sqrt{x}+4x)(x^{\frac{3}{2}}-x)
(1/(x^2))^'	(\frac{1}{x^{2}})^{\prime\:}
integral of sin(x)sec^7(x)	\int\:\sin(x)\sec^{7}(x)dx
(\partial)/(\partial z)(e^{-xyz})	\frac{\partial\:}{\partial\:z}(e^{-xyz})
derivative of (e^{3x}/3)	\frac{d}{dx}(\frac{e^{3x}}{3})
derivative of (-2x-3x^5tan(x))	\frac{d}{dx}((-2x-3x^{5})\tan(x))
limit as h approaches 0 of (7xh+h^2)/h	\lim\:_{h\to\:0}(\frac{7xh+h^{2}}{h})
derivative of sin(ln(x))	derivative\:\sin(\ln(x))
derivative of 9x^{4/3}-2/3 x^{3/2}+x^2-3x+1	derivative\:9x^{\frac{4}{3}}-\frac{2}{3}x^{\frac{3}{2}}+x^{2}-3x+1
limit as x approaches-211 of (5-x)^{2/3}	\lim\:_{x\to\:-211}((5-x)^{\frac{2}{3}})
integral from 0 to h of (L^2)/(h^2)x^2	\int\:_{0}^{h}\frac{L^{2}}{h^{2}}x^{2}dx
(dy)/(dx)=((x^2y^2))/(1+x)	\frac{dy}{dx}=\frac{(x^{2}y^{2})}{1+x}
derivative of ,x^2	\frac{d}{dx}(,x^{2})
integral of-x^{1/3}	\int\:-x^{\frac{1}{3}}dx
sum from n=1 to infinity of n/(5^n)	\sum\:_{n=1}^{\infty\:}\frac{n}{5^{n}}
integral of 8xcos(7x)	\int\:8x\cos(7x)dx
integral of (x^4-3x^{1/2}+2)/(x^{3/2)}	\int\:\frac{x^{4}-3x^{\frac{1}{2}}+2}{x^{\frac{3}{2}}}dx
derivative of f(x)=(x^3)/(5-x^2)	derivative\:f(x)=\frac{x^{3}}{5-x^{2}}
integral from 0 to 2pi of sin(x)cos^2(x)	\int\:_{0}^{2π}\sin(x)\cos^{2}(x)dx
integral of sec(y)(tan(y)-sec(y))	\int\:\sec(y)(\tan(y)-\sec(y))dy
derivative of e^{(x+1^2})	\frac{d}{dx}(e^{(x+1)^{2}})
limit as x approaches pi of ln(cos(x)-5)	\lim\:_{x\to\:π}(\ln(\cos(x)-5))
tangent of f(x)=sqrt(x^2+3),\at x= 1/2	tangent\:f(x)=\sqrt{x^{2}+3},\at\:x=\frac{1}{2}
(\partial)/(\partial y)(cos(xz))	\frac{\partial\:}{\partial\:y}(\cos(xz))
integral of (3te^{3t})	\int\:(3te^{3t})dt
integral from-2 to 1 of x^2-1	\int\:_{-2}^{1}x^{2}-1dx
(\partial)/(\partial x)(arcsin(2x-5))	\frac{\partial\:}{\partial\:x}(\arcsin(2x-5))
area x=y^2,x=36	area\:x=y^{2},x=36
limit as x approaches 0 of cos^2(x)-1	\lim\:_{x\to\:0}(\cos^{2}(x)-1)
integral of (x^2+3x+2)/(x(x^2+2x+2))	\int\:\frac{x^{2}+3x+2}{x(x^{2}+2x+2)}dx
y(1+e^x)dy+(y^4+1)dx=0	y(1+e^{x})dy+(y^{4}+1)dx=0
sum from n=1 to infinity of (sin(7))^n	\sum\:_{n=1}^{\infty\:}(\sin(7))^{n}
integral from 0 to 2 of xsqrt(9-x^2)	\int\:_{0}^{2}x\sqrt{9-x^{2}}dx
tangent of-3x^2+7x	tangent\:-3x^{2}+7x
integral of tan(x)sec^5(x)	\int\:\tan(x)\sec^{5}(x)dx
(\partial)/(\partial x)(sin(nx)e^{-ny})	\frac{\partial\:}{\partial\:x}(\sin(nx)e^{-ny})
derivative of x^8e^x	derivative\:x^{8}e^{x}
integral of x+4	\int\:x+4dx
derivative of (1+4x^2(x-x^2))	\frac{d}{dx}((1+4x^{2})(x-x^{2}))
integral of 6+6x+36x^2	\int\:6+6x+36x^{2}dx
f^'(x)=x-3	f^{\prime\:}(x)=x-3
limit as x approaches pi+of ln(tan(x))	\lim\:_{x\to\:π+}(\ln(\tan(x)))
derivative of e^{-x}+xe^{-x}	\frac{d}{dx}(e^{-x}+xe^{-x})
derivative of (7x^2-14x+14e^x)	\frac{d}{dx}((7x^{2}-14x+14)e^{x})
integral of (4x^3+4x+4)/(x^3+x)	\int\:\frac{4x^{3}+4x+4}{x^{3}+x}dx
tangent of 4(x-1/x)^2,\at x=2	tangent\:4(x-\frac{1}{x})^{2},\at\:x=2
derivative of f(x)=4x^7-5cos(x)	derivative\:f(x)=4x^{7}-5\cos(x)
integral of e^xx	\int\:e^{x}xdx
sum from n=1 to infinity of (n!)/(18^n)	\sum\:_{n=1}^{\infty\:}\frac{n!}{18^{n}}
derivative of ln(sin(11x))	derivative\:\ln(\sin(11x))
limit as x approaches-2 of x^2+3x	\lim\:_{x\to\:-2}(x^{2}+3x)
t^2y^{''}+9ty^'+16y=0	t^{2}y^{\prime\:\prime\:}+9ty^{\prime\:}+16y=0
integral from 1 to infinity of 1/(x^2+1)	\int\:_{1}^{\infty\:}\frac{1}{x^{2}+1}dx
(3-x)^'	(3-x)^{\prime\:}
derivative of 2+8x^{3/2}	derivative\:2+8x^{\frac{3}{2}}
derivative of (t^2-2)^2	derivative\:(t^{2}-2)^{2}
25y^{''}-20y^'+4y=0	25y^{\prime\:\prime\:}-20y^{\prime\:}+4y=0
integral of cos(wx)	\int\:\cos(wx)dx
x(dy)/(dx)=-1.5y	x\frac{dy}{dx}=-1.5y
limit as x approaches+0 of sqrt(4-x)	\lim\:_{x\to\:+0}(\sqrt{4-x})
(\partial)/(\partial x)(xsqrt(v-w))	\frac{\partial\:}{\partial\:x}(x\sqrt{v-w})
integral of 6sin^2(x)cos(x)	\int\:6\sin^{2}(x)\cos(x)dx
integral of 1/((x-2)(x+4))	\int\:\frac{1}{(x-2)(x+4)}dx
integral of-(9000)/((3x+50)^2)	\int\:-\frac{9000}{(3x+50)^{2}}dx
integral of 1/(y+5)	\int\:\frac{1}{y+5}dy
(\partial)/(\partial x)(yz+xz+xy)	\frac{\partial\:}{\partial\:x}(yz+xz+xy)
(\partial)/(\partial x)(8*y^{22})	\frac{\partial\:}{\partial\:x}(8\cdot\:y^{22})
y^{''}-y^'=(3x^2+6x+1)e^x	y^{\prime\:\prime\:}-y^{\prime\:}=(3x^{2}+6x+1)e^{x}
integral of x\sqrt[3]{2x+3}	\int\:x\sqrt[3]{2x+3}dx
limit as x approaches+1 of 3x^3-4x^2+x+9	\lim\:_{x\to\:+1}(3x^{3}-4x^{2}+x+9)
derivative of y=e^{x/2}	derivative\:y=e^{\frac{x}{2}}
integral of 2xye^{x+y}	\int\:2xye^{x+y}dx
integral of x^3\sqrt[3]{x^2+1}	\int\:x^{3}\sqrt[3]{x^{2}+1}dx
y^'=-yt+0.1y^'t+4	y^{\prime\:}=-yt+0.1y^{\prime\:}t+4

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