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Popular Calculus Problems

integral of (sqrt(4-x^2))/2	\int\:\frac{\sqrt{4-x^{2}}}{2}dx
derivative of x^3-9x^2+24x	\frac{d}{dx}(x^{3}-9x^{2}+24x)
sum from n=1 to infinity of (2^n)/(n^2)	\sum\:_{n=1}^{\infty\:}\frac{2^{n}}{n^{2}}
derivative of 1/(2x)-5/(3x^2)	derivative\:\frac{1}{2x}-\frac{5}{3x^{2}}
integral of 11arcsin(sqrt(2x))	\int\:11\arcsin(\sqrt{2x})dx
integral of (e^{-10x})	\int\:(e^{-10x})dx
limit as x approaches 0 of (x4^x)/(4^x-1)	\lim\:_{x\to\:0}(\frac{x4^{x}}{4^{x}-1})
integral of (pisin(pi)x)	\int\:(π\sin(π)x)dx
limit as x approaches 0+of (1-2x)^{1/x}	\lim\:_{x\to\:0+}((1-2x)^{\frac{1}{x}})
area 4x^2+y=4,x^4-y=1	area\:4x^{2}+y=4,x^{4}-y=1
limit as x approaches infinity+of (x^5-3x^2+5x-9)/(7x^4-6x^2+5x-9)	\lim\:_{x\to\:\infty\:+}(\frac{x^{5}-3x^{2}+5x-9}{7x^{4}-6x^{2}+5x-9})
derivative of e^{ln(3})	\frac{d}{dx}(e^{\ln(3)})
derivative of y=x^2-3x+3	derivative\:y=x^{2}-3x+3
integral of 1/(sqrt(2-3x-4x^2))	\int\:\frac{1}{\sqrt{2-3x-4x^{2}}}dx
f(x)=e^{2x}-e^{-2x}	f(x)=e^{2x}-e^{-2x}
f^'(x)=4sin^2(x)	f^{\prime\:}(x)=4\sin^{2}(x)
limit as h approaches 0-of 1/(h^2+1)	\lim\:_{h\to\:0-}(\frac{1}{h^{2}+1})
integral of e^{-x/(11)}	\int\:e^{-\frac{x}{11}}dx
x((dy)/(dx))=y+xe^{y/x}	x(\frac{dy}{dx})=y+xe^{\frac{y}{x}}
area y= 2/(1+x^2),y=1	area\:y=\frac{2}{1+x^{2}},y=1
derivative of f(x)=sqrt(3x+1)	derivative\:f(x)=\sqrt{3x+1}
(\partial)/(\partial x)(10)	\frac{\partial\:}{\partial\:x}(10)
(\partial)/(\partial y)(x^2+2y^2+3xz)	\frac{\partial\:}{\partial\:y}(x^{2}+2y^{2}+3xz)
limit as x approaches-2 of 1/(x+1)	\lim\:_{x\to\:-2}(\frac{1}{x+1})
integral of 4/(xln(5x))	\int\:\frac{4}{x\ln(5x)}dx
integral of 1/((441+x^2)^{3/2)}	\int\:\frac{1}{(441+x^{2})^{\frac{3}{2}}}dx
x^'=k(300-x)	x^{\prime\:}=k(300-x)
derivative of (8x^3-9/(x^2))	\frac{d}{dx}(\frac{8x^{3}-9}{x^{2}})
integral of 1/(u^5)	\int\:\frac{1}{u^{5}}du
derivative of 4cos(x-sin(x))	\frac{d}{dx}(4\cos(x)-\sin(x))
x^2y^{''}-3xy^'+3y=0,y(1)=5,y^'(1)=3	x^{2}y^{\prime\:\prime\:}-3xy^{\prime\:}+3y=0,y(1)=5,y^{\prime\:}(1)=3
x(e^{y/x}-1)y^'=e^{y/x}(y-x)	x(e^{\frac{y}{x}}-1)y^{\prime\:}=e^{\frac{y}{x}}(y-x)
derivative of y=ln(x^5)+e^x-ln(e^2)	derivative\:y=\ln(x^{5})+e^{x}-\ln(e^{2})
derivative of y=(3x+1)^2	derivative\:y=(3x+1)^{2}
derivative of-y+x+2	\frac{d}{dx}(-y+x+2)
integral of (sec^2(sqrt(x)))/(2sqrt(x))	\int\:\frac{\sec^{2}(\sqrt{x})}{2\sqrt{x}}dx
derivative of (x-1)*ln(x-1)	derivative\:(x-1)\cdot\:\ln(x-1)
limit as x approaches 0 of (x^3+3x)/x	\lim\:_{x\to\:0}(\frac{x^{3}+3x}{x})
integral of tan^3(θ)sec^2(θ)	\int\:\tan^{3}(θ)\sec^{2}(θ)dθ
integral of 3/5-6/x	\int\:\frac{3}{5}-\frac{6}{x}dx
(\partial)/(\partial x)(inx)	\frac{\partial\:}{\partial\:x}(inx)
integral of xcos(pi)x	\int\:x\cos(π)xdx
area y=sqrt(x),y=0,x=4	area\:y=\sqrt{x},y=0,x=4
(dy)/(dx)=x^2y^2+x^2+y^2+1	\frac{dy}{dx}=x^{2}y^{2}+x^{2}+y^{2}+1
integral from 0 to 1 of (e^{(2x)/3}+1)	\int\:_{0}^{1}(e^{\frac{2x}{3}}+1)dx
y^{''}+(2*0.1096)y^'+(4.515^2)y=0	y^{\prime\:\prime\:}+(2\cdot\:0.1096)y^{\prime\:}+(4.515^{2})y=0
(t^2+9)y^'+2ty=t^2(t^2+9)	(t^{2}+9)y^{\prime\:}+2ty=t^{2}(t^{2}+9)
integral of+x/(x^2+9)	\int\:+\frac{x}{x^{2}+9}dx
derivative of 18xe^x	\frac{d}{dx}(18xe^{x})
(\partial)/(\partial x)(sqrt((x+4)/(y+3)))	\frac{\partial\:}{\partial\:x}(\sqrt{\frac{x+4}{y+3}})
derivative of 144((216)/(x^2)+x/(x+24))	derivative\:144(\frac{216}{x^{2}}+\frac{x}{x+24})
y^'=e^xy^7+2y	y^{\prime\:}=e^{x}y^{7}+2y
integral of (ln(sqrt(x+1)))/(x+1)	\int\:\frac{\ln(\sqrt{x+1})}{x+1}dx
(dy)/(dt)=sin(2pi(t+3))	\frac{dy}{dt}=\sin(2π(t+3))
integral from 0 to 2 of 2piy(2y-y^2)	\int\:_{0}^{2}2πy(2y-y^{2})dy
taylor e^{3x}	taylor\:e^{3x}
x((dy)/(dx))=4y	x(\frac{dy}{dx})=4y
laplacetransform {6e^{-3t}-t^2+2t-8}	laplacetransform\:\left\{6e^{-3t}-t^{2}+2t-8\right\}
(y-x)e^x+(1+e^x)(dy)/(dx)=0	(y-x)e^{x}+(1+e^{x})\frac{dy}{dx}=0
integral from 0 to 1 of 2pix(sqrt(x)-x)	\int\:_{0}^{1}2πx(\sqrt{x}-x)dx
integral from 1 to 7 of (6x^2+2x-3)	\int\:_{1}^{7}(6x^{2}+2x-3)dx
sum from n=10 to infinity of 2/3 (3/4)^n	\sum\:_{n=10}^{\infty\:}\frac{2}{3}(\frac{3}{4})^{n}
integral of (1+sqrt(x))^8	\int\:(1+\sqrt{x})^{8}dx
tangent of (7x)/(x-1)	tangent\:\frac{7x}{x-1}
integral from 0 to infinity of xe^{-xy}	\int\:_{0}^{\infty\:}xe^{-xy}dx
derivative of (sqrt(x))(3-x)^2	derivative\:(\sqrt{x})(3-x)^{2}
derivative of ycos(xln(y))	\frac{d}{dx}(y\cos(x\ln(y)))
simplify x/(2-sqrt(x))	simplify\:\frac{x}{2-\sqrt{x}}
(dy)/(dx)=5(1-x/(10))	\frac{dy}{dx}=5(1-\frac{x}{10})
integral from-2 to 0 of-sqrt(x+2)	\int\:_{-2}^{0}-\sqrt{x+2}dx
integral of-20x^{-5}	\int\:-20x^{-5}dx
(dy)/(dx)=e^{y-x}	\frac{dy}{dx}=e^{y-x}
derivative of x^2(x+1)	\frac{d}{dx}(x^{2}(x+1))
(d^2)/(dx^2)(sqrt(x)ln(x))	\frac{d^{2}}{dx^{2}}(\sqrt{x}\ln(x))
derivative of-(0.1x-23)^2	derivative\:-(0.1x-23)^{2}
integral of 2e^{-3t}	\int\:2e^{-3t}dt
derivative of sqrt(\sqrt{4x+3)}	derivative\:\sqrt{\sqrt{4x+3}}
slope ofintercept (-4,2),(6,-3)	slopeintercept\:(-4,2),(6,-3)
derivative of 1/(sqrt(1+e^{4x)})	\frac{d}{dx}(\frac{1}{\sqrt{1+e^{4x}}})
limit as x approaches 0+of (x+\|x\|)/x	\lim\:_{x\to\:0+}(\frac{x+\left\|x\right\|}{x})
limit as x approaches 4 of x^3+6x^2-5x-1	\lim\:_{x\to\:4}(x^{3}+6x^{2}-5x-1)
derivative of (1-3x/(2+x))	\frac{d}{dx}(\frac{1-3x}{2+x})
integral of sec^5(x)	\int\:\sec^{5}(x)dx
tangent of f(x)=xsqrt(x),\at x=0	tangent\:f(x)=x\sqrt{x},\at\:x=0
integral of 1/(x^2+8x+32)	\int\:\frac{1}{x^{2}+8x+32}dx
limit as x approaches 7-of x/(x^2-49)	\lim\:_{x\to\:7-}(\frac{x}{x^{2}-49})
area x+1,9-x^2,-1,2	area\:x+1,9-x^{2},-1,2
y^'=(x+y)^2-1,y(1)=6	y^{\prime\:}=(x+y)^{2}-1,y(1)=6
limit as x approaches 1-of x^3	\lim\:_{x\to\:1-}(x^{3})
derivative of sin(7ln(x))	derivative\:\sin(7\ln(x))
integral of sin^3(x)cos^9(x)	\int\:\sin^{3}(x)\cos^{9}(x)dx
(\partial)/(\partial x)(x/(sqrt(y-x)))	\frac{\partial\:}{\partial\:x}(\frac{x}{\sqrt{y-x}})
(\partial)/(\partial x)(sqrt(x+yz))	\frac{\partial\:}{\partial\:x}(\sqrt{x+yz})
integral from 1 to 2 of (13)/(x^3+2x)	\int\:_{1}^{2}\frac{13}{x^{3}+2x}dx
integral of (2x+1)/(sqrt(x))	\int\:\frac{2x+1}{\sqrt{x}}dx
(\partial)/(\partial x)(e^{xy}cos(x^2))	\frac{\partial\:}{\partial\:x}(e^{xy}\cos(x^{2}))
xy^2dy=(y^3-x^3)dx	xy^{2}dy=(y^{3}-x^{3})dx
d/(dθ)(sqrt(1+sin(2θ)))	\frac{d}{dθ}(\sqrt{1+\sin(2θ)})
integral of cot^2(3x)csc^4(3x)	\int\:\cot^{2}(3x)\csc^{4}(3x)dx
limit as x approaches 0 of xln(sin(x))	\lim\:_{x\to\:0}(x\ln(\sin(x)))

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