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Popular Calculus Problems

integral of (11x^2)/((225+x^2)^2)	\int\:\frac{11x^{2}}{(225+x^{2})^{2}}dx
integral of (sin(3x))/([1+cos(3x)]^4)	\int\:\frac{\sin(3x)}{[1+\cos(3x)]^{4}}dx
derivative of 3x^2-5x+1	derivative\:3x^{2}-5x+1
limit as x approaches 0 of 3sin(x)-2	\lim\:_{x\to\:0}(3\sin(x)-2)
integral of sin(3x)*cos(3x)	\int\:\sin(3x)\cdot\:\cos(3x)dx
integral of e^y-1	\int\:e^{y}-1dy
derivative of (x-1/x ^{5/2})	\frac{d}{dx}((x-\frac{1}{x})^{\frac{5}{2}})
(\partial)/(\partial x)(4sin(xy))	\frac{\partial\:}{\partial\:x}(4\sin(xy))
derivative of y=((2x-3)/((x^2+4)^2))	derivative\:y=(\frac{2x-3}{(x^{2}+4)^{2}})
slope ofintercept (1,4),(4,1)	slopeintercept\:(1,4),(4,1)
sum from n=0 to infinity of ((n!)^2)/(2^{n^2)}	\sum\:_{n=0}^{\infty\:}\frac{(n!)^{2}}{2^{n^{2}}}
derivative of y=(2x+e^{-x^2})^3	derivative\:y=(2x+e^{-x^{2}})^{3}
(dP)/(dt)=P(a-bP)	\frac{dP}{dt}=P(a-bP)
area y=2x,y=2x^2-4	area\:y=2x,y=2x^{2}-4
derivative of \|2x+1\|	\frac{d}{dx}(\left\|2x+1\right\|)
integral from 1 to 8 of 2/(x^3)	\int\:_{1}^{8}\frac{2}{x^{3}}dx
(\partial)/(\partial x)((\sqrt[7]{x})^4)	\frac{\partial\:}{\partial\:x}((\sqrt[7]{x})^{4})
limit as x approaches 0+of (-ln(x))^x	\lim\:_{x\to\:0+}((-\ln(x))^{x})
derivative of x^2sqrt(x^4-12)	\frac{d}{dx}(x^{2}\sqrt{x^{4}-12})
(dy)/(dx)=((3x^2))/(y^2)	\frac{dy}{dx}=\frac{(3x^{2})}{y^{2}}
derivative of x-sin(2x)	\frac{d}{dx}(x-\sin(2x))
limit as x approaches-2 of x(2)	\lim\:_{x\to\:-2}(x(2))
(\partial)/(\partial y)(x^2sin(y))	\frac{\partial\:}{\partial\:y}(x^{2}\sin(y))
(\partial)/(\partial y)(2e^x)	\frac{\partial\:}{\partial\:y}(2e^{x})
d/(dt)(sec(t)tan(t))	\frac{d}{dt}(\sec(t)\tan(t))
derivative of-2cot(x+3csc(x))	\frac{d}{dx}(-2\cot(x)+3\csc(x))
area y=5cos(x),y=5sin(x),0<= x<= pi	area\:y=5\cos(x),y=5\sin(x),0\le\:x\le\:π
derivative of (x^2-1^{1/3})	\frac{d}{dx}((x^{2}-1)^{\frac{1}{3}})
integral of 0sin(nx)	\int\:0\sin(nx)dx
f(x)=0.1x^3-0.45x^2+2.43x+300	f(x)=0.1x^{3}-0.45x^{2}+2.43x+300
derivative of 3/(x^2-4)	\frac{d}{dx}(\frac{3}{x^{2}-4})
derivative of 7xsin(x^2)	derivative\:7x\sin(x^{2})
integral of-cos(x)+sin(x)+4	\int\:-\cos(x)+\sin(x)+4dx
integral of (csc^2(x))/(cot(x)+1)	\int\:\frac{\csc^{2}(x)}{\cot(x)+1}dx
tangent of f(x)=(2+5x)(5-4x),\at x=1	tangent\:f(x)=(2+5x)(5-4x),\at\:x=1
y^'-y=5.2	y^{\prime\:}-y=5.2
integral of sin(3z)cos(2)(3z)	\int\:\sin(3z)\cos(2)(3z)dz
tangent of f(t)=tcos(2t)e^{-t},\at t=3	tangent\:f(t)=t\cos(2t)e^{-t},\at\:t=3
(1+x^2+y^2+x^2y^2)dy=y^2dx	(1+x^{2}+y^{2}+x^{2}y^{2})dy=y^{2}dx
integral of 1/(sqrt(3x-2))	\int\:\frac{1}{\sqrt{3x-2}}dx
derivative of f(x)=(9x^3+3x^2)^4	derivative\:f(x)=(9x^{3}+3x^{2})^{4}
derivative of sqrt(6+tan^2(x))	\frac{d}{dx}(\sqrt{6+\tan^{2}(x)})
derivative of (18/(x^4))	\frac{d}{dx}(\frac{18}{x^{4}})
integral of 1/(sec^2(u))	\int\:\frac{1}{\sec^{2}(u)}du
integral from 0 to 4 of \|2x-3\|	\int\:_{0}^{4}\left\|2x-3\right\|dx
inverse oflaplace s/(s+1/2)	inverselaplace\:\frac{s}{s+\frac{1}{2}}
maclaurin e^{-x},5	maclaurin\:e^{-x},5
integral of 1+2/y	\int\:1+\frac{2}{y}dy
derivative of 1/(2z^3)	derivative\:\frac{1}{2z^{3}}
y^'=-(2y)/(x+1)+2x	y^{\prime\:}=-\frac{2y}{x+1}+2x
limit as x approaches 4 of x^2-1	\lim\:_{x\to\:4}(x^{2}-1)
integral of xln^5(x)	\int\:x\ln^{5}(x)dx
derivative of f(x)=x^4sin(4x)	derivative\:f(x)=x^{4}\sin(4x)
integral from 1 to 2 of 1	\int\:_{1}^{2}1
sum from n=0 to infinity of (pi^n)/(e^n)	\sum\:_{n=0}^{\infty\:}\frac{π^{n}}{e^{n}}
limit as t approaches 1 of 7e^t-3	\lim\:_{t\to\:1}(7e^{t}-3)
integral from 1 to e of ln(6x)	\int\:_{1}^{e}\ln(6x)dx
area y=(x^2+4)/(3x-x^2),(1,2)	area\:y=\frac{x^{2}+4}{3x-x^{2}},(1,2)
derivative of (arccot(x))^5	derivative\:(\arccot(x))^{5}
integral of 3sin(3x)	\int\:3\sin(3x)dx
derivative of 3cos(x-5cot(x))	\frac{d}{dx}(3\cos(x)-5\cot(x))
(xy^2)dx+(1+x^2y)dy=0	(xy^{2})dx+(1+x^{2}y)dy=0
derivative of sqrt((4+8/x ^2+(2+x)^2))	\frac{d}{dx}(\sqrt{(4+\frac{8}{x})^{2}+(2+x)^{2}})
area y=sqrt(x^2-1),x=1,x=3	area\:y=\sqrt{x^{2}-1},x=1,x=3
integral of 3xln(4x)	\int\:3x\ln(4x)dx
derivative of f(x)=(3-5x)^9	derivative\:f(x)=(3-5x)^{9}
derivative of cos^2((a-x^3))	\frac{d}{dx}(\cos^{2}((a-x)^{3}))
integral of 7\sqrt[4]{58-7x}-14	\int\:7\sqrt[4]{58-7x}-14dx
laplacetransform t^2cos(8t)	laplacetransform\:t^{2}\cos(8t)
derivative of x^3-8x^2+31x	\frac{d}{dx}(x^{3}-8x^{2}+31x)
(d^2)/(dx^2)(x^2e^x)	\frac{d^{2}}{dx^{2}}(x^{2}e^{x})
sum from n=0 to infinity of-3^n	\sum\:_{n=0}^{\infty\:}-3^{n}
tangent of 7/(sqrt(x))	tangent\:\frac{7}{\sqrt{x}}
integral of 1/(sqrt(-x^2+4x-1))	\int\:\frac{1}{\sqrt{-x^{2}+4x-1}}dx
tangent of y=x^2-12x+4	tangent\:y=x^{2}-12x+4
integral of e^tsin(3t)	\int\:e^{t}\sin(3t)dt
derivative of 2tan^2(4x)	derivative\:2\tan^{2}(4x)
(\partial)/(\partial x)(x^2sqrt(y))	\frac{\partial\:}{\partial\:x}(x^{2}\sqrt{y})
y=log_{3}(sin(x^2))	y=\log_{3}(\sin(x^{2}))
y^'+2y=xy^{-2}	y^{\prime\:}+2y=xy^{-2}
derivative of (x-1^{2x})	\frac{d}{dx}((x-1)^{2x})
derivative of 10arctan(x)	\frac{d}{dx}(10\arctan(x))
limit as x approaches-2 of 4-x	\lim\:_{x\to\:-2}(4-x)
(dy)/(dx)=(x+y+3)^2	\frac{dy}{dx}=(x+y+3)^{2}
integral from-3 to-1 of 2x^2+3	\int\:_{-3}^{-1}2x^{2}+3dx
derivative of e^p(p+sqrt(p))	derivative\:e^{p}(p+\sqrt{p})
integral of t/((t+1)^4)	\int\:\frac{t}{(t+1)^{4}}dt
x*ln(x)=y(1+sqrt(3+y^2))y^'(x),y(1)=1	x\cdot\:\ln(x)=y(1+\sqrt{3+y^{2}})y^{\prime\:}(x),y(1)=1
(dy)/(dx)=0.0017y(3000-y)	\frac{dy}{dx}=0.0017y(3000-y)
derivative of xe^{5x}cos(2x)	\frac{d}{dx}(xe^{5x}\cos(2x))
derivative of f(x)=10	derivative\:f(x)=10
(\partial)/(\partial y)(xln(x/y)+xy^2)	\frac{\partial\:}{\partial\:y}(x\ln(\frac{x}{y})+xy^{2})
integral of 3-x	\int\:3-xdx
laplacetransform 15t^4e^{4t}+10	laplacetransform\:15t^{4}e^{4t}+10
6t(dy)/(dt)+4y=sqrt(t)	6t\frac{dy}{dt}+4y=\sqrt{t}
integral of e^x(sin(e^x))	\int\:e^{x}(\sin(e^{x}))dx
derivative of-4cos^2(x)	\frac{d}{dx}(-4\cos^{2}(x))
sum from n=1 to infinity of e/pi	\sum\:_{n=1}^{\infty\:}\frac{e}{π}
derivative of p(h)=30e^{-0.0000323h}	derivative\:p(h)=30e^{-0.0000323h}
integral from 0 to 5 of (x-3)/(x^2-5x-6)	\int\:_{0}^{5}\frac{x-3}{x^{2}-5x-6}dx

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