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Popular Calculus Problems

integral of (35)/(1-cos(5x))	\int\:\frac{35}{1-\cos(5x)}dx
derivative of x^5+x+1	\frac{d}{dx}(x^{5}+x+1)
derivative of (((0.06x^2+17x+340))/x)	\frac{d}{dx}(\frac{((0.06x^{2})+17x+340)}{x})
laplacetransform 2e^{t/2}	laplacetransform\:2e^{\frac{t}{2}}
integral from 2 to t of 1/((5x^5))	\int\:_{2}^{t}\frac{1}{(5x^{5})}dx
integral of 1/(P-P^2)	\int\:\frac{1}{P-P^{2}}dP
integral of x/(x+4)	\int\:\frac{x}{x+4}dx
tangent of f(x)=(2x)/(x^2-7),(3,3)	tangent\:f(x)=\frac{2x}{x^{2}-7},(3,3)
(x^2+1)y^'+9x(y-1)=0	(x^{2}+1)y^{\prime\:}+9x(y-1)=0
integral of (cos(x))^4	\int\:(\cos(x))^{4}dx
derivative of f(x)=(x-3)/(x+4)	derivative\:f(x)=\frac{x-3}{x+4}
laplacetransform t^2-4t+4	laplacetransform\:t^{2}-4t+4
xdx+ydy=xy(xdy-ydx)	xdx+ydy=xy(xdy-ydx)
derivative of-6x^{1/4}	\frac{d}{dx}(-6x^{\frac{1}{4}})
integral of 1/(x(x-1))	\int\:\frac{1}{x(x-1)}dx
limit as x approaches 1 of 1/(2x-1)	\lim\:_{x\to\:1}(\frac{1}{2x-1})
(\partial)/(\partial x)(x/(sqrt(x^2+y^3)))	\frac{\partial\:}{\partial\:x}(\frac{x}{\sqrt{x^{2}+y^{3}}})
y^'+7=e^{7x+y-5},y(0)=5	y^{\prime\:}+7=e^{7x+y-5},y(0)=5
area 1/4 x^2-1,0,2,8	area\:\frac{1}{4}x^{2}-1,0,2,8
y=2sin(x)	y=2\sin(x)
derivative of sqrt(arctan(x/2))	\frac{d}{dx}(\sqrt{\arctan(\frac{x}{2})})
(\partial)/(\partial y)((2x)/(y^2))	\frac{\partial\:}{\partial\:y}(\frac{2x}{y^{2}})
y^'=8(y^2+1)	y^{\prime\:}=8(y^{2}+1)
f(x)=6x^{1/2}	f(x)=6x^{\frac{1}{2}}
integral of cos(5x-1)	\int\:\cos(5x-1)dx
integral of 3xsqrt(x+5)	\int\:3x\sqrt{x+5}dx
13(t+1)(dy)/(dt)-9y=36t	13(t+1)\frac{dy}{dt}-9y=36t
integral of xcos(10x)	\int\:x\cos(10x)dx
derivative of arcsec(1/x)	\frac{d}{dx}(\arcsec(\frac{1}{x}))
integral of 200sin(5x)\sqrt[3]{cos(5x)}	\int\:200\sin(5x)\sqrt[3]{\cos(5x)}dx
integral of 1-ln(x)	\int\:1-\ln(x)dx
integral of (6x-11)/((x-1)^2)	\int\:\frac{6x-11}{(x-1)^{2}}dx
laplacetransform x^2	laplacetransform\:x^{2}
integral of 1/(sqrt(12+4x-x^2))	\int\:\frac{1}{\sqrt{12+4x-x^{2}}}dx
integral of csc(ay)cot(ay)	\int\:\csc(ay)\cot(ay)dy
derivative of (x^2-1)/((2x-5)^2)	derivative\:\frac{x^{2}-1}{(2x-5)^{2}}
derivative of 4cos(sin(3x))	\frac{d}{dx}(4\cos(\sin(3x)))
y^{'''}+y^'=t^2	y^{\prime\:\prime\:\prime\:}+y^{\prime\:}=t^{2}
limit as t approaches 0 of (sin(4t))/t	\lim\:_{t\to\:0}(\frac{\sin(4t)}{t})
derivative of 65x^{9/10}	derivative\:65x^{\frac{9}{10}}
integral of cos(x)csc^6(x)	\int\:\cos(x)\csc^{6}(x)dx
integral of 1/(3+y)	\int\:\frac{1}{3+y}dy
integral from 0 to 1 of 1/(1+9x^2)	\int\:_{0}^{1}\frac{1}{1+9x^{2}}dx
(dP)/(dt)=0.2P-0.001P^2	\frac{dP}{dt}=0.2P-0.001P^{2}
derivative of-(2e^x/(x^3)+(e^x)/(x^2))	\frac{d}{dx}(-\frac{2e^{x}}{x^{3}}+\frac{e^{x}}{x^{2}})
derivative of sin(xcos(2x))	\frac{d}{dx}(\sin(x)\cos(2x))
derivative of ln(3x^2+4)	\frac{d}{dx}(\ln(3x^{2}+4))
derivative of 24x^{3/2}	\frac{d}{dx}(24x^{\frac{3}{2}})
simplify (2x)/(sqrt(x^2+1))	simplify\:\frac{2x}{\sqrt{x^{2}+1}}
f(x)=xsqrt(2)	f(x)=x\sqrt{2}
integral of ((ln(z))^6)/z	\int\:\frac{(\ln(z))^{6}}{z}dz
(d^2)/(dx^2)(cos(x^2))	\frac{d^{2}}{dx^{2}}(\cos(x^{2}))
(\partial)/(\partial x)((4x^3y^4+9)^2)	\frac{\partial\:}{\partial\:x}((4x^{3}y^{4}+9)^{2})
integral from 0 to 1 of 2pi(2-y)(2-2y^2)	\int\:_{0}^{1}2π(2-y)(2-2y^{2})dy
derivative of 5sin(10x)	\frac{d}{dx}(5\sin(10x))
derivative of 10sin^3(x)	\frac{d}{dx}(10\sin^{3}(x))
integral of (3^x)/(ln(3))	\int\:\frac{3^{x}}{\ln(3)}dx
derivative of (cot(x)/x)	\frac{d}{dx}(\frac{\cot(x)}{x})
derivative of (3+xf(x))/(sqrt(x))	derivative\:\frac{3+xf(x)}{\sqrt{x}}
derivative of ln(1-(10/x))	\frac{d}{dx}(\ln(1-\frac{10}{x}))
derivative of f(x)=sqrt(5x+1)	derivative\:f(x)=\sqrt{5x+1}
derivative of f(x)=((tan(x)-1))/(sec(x))	derivative\:f(x)=\frac{(\tan(x)-1)}{\sec(x)}
integral from 0 to 2 of x^2	\int\:_{0}^{2}x^{2}dx
derivative of 2/(e^x+e^{-x})	\frac{d}{dx}(\frac{2}{e^{x}+e^{-x}})
integral of ((x^2+2x+3))/((x^3+3x^2+9x))	\int\:\frac{(x^{2}+2x+3)}{(x^{3}+3x^{2}+9x)}dx
integral from 0 to 2pi of sin^2(4x)	\int\:_{0}^{2π}\sin^{2}(4x)dx
integral of (e^x)/3	\int\:\frac{e^{x}}{3}dx
integral of cos(3xy)	\int\:\cos(3xy)dx
d/(dt)(tan(3t))	\frac{d}{dt}(\tan(3t))
sum from n=1 to infinity of 2/(3^{2n)}	\sum\:_{n=1}^{\infty\:}\frac{2}{3^{2n}}
y^{'''}+4y^'=sec(2x)	y^{\prime\:\prime\:\prime\:}+4y^{\prime\:}=\sec(2x)
limit as x approaches 0 of 3pi	\lim\:_{x\to\:0}(3π)
f(θ)=4cos(θ)	f(θ)=4\cos(θ)
integral of 4xe^{2/3 x}	\int\:4xe^{\frac{2}{3}x}dx
derivative of x/((x^2+1^{1/2)})	\frac{d}{dx}(\frac{x}{(x^{2}+1)^{\frac{1}{2}}})
(d^2)/(dx^2)((2x^2+7)^5)	\frac{d^{2}}{dx^{2}}((2x^{2}+7)^{5})
derivative of In,x^2	\frac{d}{dx}(In,x^{2})
(dP)/(dt)=kP	\frac{dP}{dt}=kP
f(x)=4tan(x)	f(x)=4\tan(x)
limit as x approaches 0+of 7sin(x)ln(x)	\lim\:_{x\to\:0+}(7\sin(x)\ln(x))
expand 8/((1-x)^2)	expand\:\frac{8}{(1-x)^{2}}
integral of (3(x+2))/((x+7)^4)	\int\:\frac{3(x+2)}{(x+7)^{4}}dx
derivative of cos^2(pix)	\frac{d}{dx}(\cos^{2}(πx))
integral from 0 to 1 of-(5y)/(e^{2y)}	\int\:_{0}^{1}-\frac{5y}{e^{2y}}dy
area-x^3+x,x=-1,y=-1/2	area\:-x^{3}+x,x=-1,y=-\frac{1}{2}
(dy)/(dt)=-y/t-7	\frac{dy}{dt}=-\frac{y}{t}-7
derivative of 2/((1-x^3))	\frac{d}{dx}(\frac{2}{(1-x)^{3}})
(\partial)/(\partial x)(z*log_{e}(x^2+y^2))	\frac{\partial\:}{\partial\:x}(z\cdot\:\log_{e}(x^{2}+y^{2}))
derivative of ln(e^{2x})	derivative\:\ln(e^{2x})
integral of 1/a	\int\:\frac{1}{a}da
simplify (4x^3+3x^2)/x	simplify\:\frac{4x^{3}+3x^{2}}{x}
limit as x approaches 1 of 3*a+x	\lim\:_{x\to\:1}(3\cdot\:a+x)
integral of 1/((121+x^2)^{3/2)}	\int\:\frac{1}{(121+x^{2})^{\frac{3}{2}}}dx
integral of ((2x^2-x+4))/(x^3+4x)	\int\:\frac{(2x^{2}-x+4)}{x^{3}+4x}dx
limit as x approaches 2 of (x^3+x^2-8x-12)/(x^4+4x^3+5x^2+4x+4)	\lim\:_{x\to\:2}(\frac{x^{3}+x^{2}-8x-12}{x^{4}+4x^{3}+5x^{2}+4x+4})
y^'=((t^4+y^4))/(ty^3)	y^{\prime\:}=\frac{(t^{4}+y^{4})}{ty^{3}}
limit as x approaches+0 of x	\lim\:_{x\to\:+0}(x)
integral of (2x+3)^4	\int\:(2x+3)^{4}dx
integral of e^{uv}	\int\:e^{uv}du
derivative of 4x^5-10x^4+2	\frac{d}{dx}(4x^{5}-10x^{4}+2)

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