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Popular Calculus Problems

d/(dθ)((1+2sin(θ))sin(θ))	\frac{d}{dθ}((1+2\sin(θ))\sin(θ))
integral of t^2sqrt(1+t^3)	\int\:t^{2}\sqrt{1+t^{3}}dt
integral of 1/(sec(sqrt(y)))	\int\:\frac{1}{\sec(\sqrt{y})}dy
integral of ((x^2+4))/(x+2)	\int\:\frac{(x^{2}+4)}{x+2}dx
integral of 1/(sin(x)+3cos(x)+1)	\int\:\frac{1}{\sin(x)+3\cos(x)+1}dx
derivative of sqrt(sin(e^{x^3sin(x))})	\frac{d}{dx}(\sqrt{\sin(e^{x^{3}\sin(x)})})
derivative of x^2-8x+12	\frac{d}{dx}(x^{2}-8x+12)
integral of 1/(8-3x)	\int\:\frac{1}{8-3x}dx
integral from 0 to 1 of-ln(x)	\int\:_{0}^{1}-\ln(x)dx
(dy)/(dx)=-y(x+1)	\frac{dy}{dx}=-y(x+1)
derivative of x+4sqrt(x+2)	derivative\:x+4\sqrt{x+2}
limit as x approaches 3 of (1/3 sqrt(x)-sqrt(1/3))/(x-3)	\lim\:_{x\to\:3}(\frac{\frac{1}{3}\sqrt{x}-\sqrt{\frac{1}{3}}}{x-3})
derivative of 8cos(x)	derivative\:8\cos(x)
derivative of sqrt(2t+1)	derivative\:\sqrt{2t+1}
limit as x approaches infinity of x^2-25	\lim\:_{x\to\:\infty\:}(x^{2}-25)
(dy)/(dx)+8y=6	\frac{dy}{dx}+8y=6
laplacetransform 2-t	laplacetransform\:2-t
derivative of (2x+5)^3(x^5+3)^6	derivative\:(2x+5)^{3}(x^{5}+3)^{6}
integral of (16x)/(sqrt(1-x^4))	\int\:\frac{16x}{\sqrt{1-x^{4}}}dx
derivative of sqrt(x^3+5)	\frac{d}{dx}(\sqrt{x^{3}+5})
(dy)/(dx)=8xe^{7y}	\frac{dy}{dx}=8xe^{7y}
integral of (-7)/(sqrt(x^2+16))	\int\:\frac{-7}{\sqrt{x^{2}+16}}dx
limit as x approaches 5 of ((ln(x/5)))/(x^2-25)	\lim\:_{x\to\:5}(\frac{(\ln(\frac{x}{5}))}{x^{2}-25})
integral of 1/(ln(x^x))	\int\:\frac{1}{\ln(x^{x})}dx
integral of x/(12)	\int\:\frac{x}{12}dx
limit as x approaches-2 of (x^2)/(x-1)	\lim\:_{x\to\:-2}(\frac{x^{2}}{x-1})
derivative of (sin(x^2))/(x^2)	derivative\:\frac{\sin(x^{2})}{x^{2}}
integral of (1+sqrt(x)+x)/(sqrt(x))	\int\:\frac{1+\sqrt{x}+x}{\sqrt{x}}dx
(dy}{dx}=\frac{13x)/y	\frac{dy}{dx}=\frac{13x}{y}
derivative of x\|x\|	derivative\:x\left\|x\right\|
integral of (3x)/1	\int\:\frac{3x}{1}dx
sum from n=1 to infinity of 2n+1	\sum\:_{n=1}^{\infty\:}2n+1
limit as x approaches 1/2 of xtan(pi)x	\lim\:_{x\to\:\frac{1}{2}}(x\tan(π)x)
limit as x approaches 3/2 of (8x^3-27)/(2x-3)	\lim\:_{x\to\:\frac{3}{2}}(\frac{8x^{3}-27}{2x-3})
derivative of x^2e^x+2xe^x	\frac{d}{dx}(x^{2}e^{x}+2xe^{x})
limit as x approaches infinity of (ln(5))/((1+ln(x)))	\lim\:_{x\to\:\infty\:}(\frac{\ln(5)}{(1+\ln(x))})
limit as x approaches 0+of sqrt(x)e^{sin(pi/x)}	\lim\:_{x\to\:0+}(\sqrt{x}e^{\sin(\frac{π}{x})})
derivative of ((10+x/pi)^{1/3})	\frac{d}{dx}((\frac{10+x}{π})^{\frac{1}{3}})
integral of-1/(1-x)	\int\:-\frac{1}{1-x}dx
integral from 2 to infinity of (8cos(pi/x))/(x^2)	\int\:_{2}^{\infty\:}\frac{8\cos(\frac{π}{x})}{x^{2}}dx
limit as h approaches+0 of (1/(a+h)-1/a)/h	\lim\:_{h\to\:+0}(\frac{\frac{1}{a+h}-\frac{1}{a}}{h})
d/(dt)(sqrt(t))	\frac{d}{dt}(\sqrt{t})
integral of t^{-3}	\int\:t^{-3}dt
integral of (x^3)/(sqrt(25+x^2))	\int\:\frac{x^{3}}{\sqrt{25+x^{2}}}dx
tangent of f(x)=-3x^2+12,\at x=3	tangent\:f(x)=-3x^{2}+12,\at\:x=3
8x^2y+y^'=10x^2	8x^{2}y+y^{\prime\:}=10x^{2}
derivative of 4x^3-33x^2+84x-60	derivative\:4x^{3}-33x^{2}+84x-60
derivative of 2xsqrt(16-x^2)	\frac{d}{dx}(2x\sqrt{16-x^{2}})
(\partial)/(\partial x)(2x^2+y^3)	\frac{\partial\:}{\partial\:x}(2x^{2}+y^{3})
derivative of f(x)=(2x^{3/2}-x^2+4)/x	derivative\:f(x)=\frac{2x^{\frac{3}{2}}-x^{2}+4}{x}
derivative of (500)/(12+5e^{-0.5t)}	derivative\:\frac{500}{12+5e^{-0.5t}}
implicit (dy)/(dx),x=y^3-8y^2+5,(-2,1)	implicit\:\frac{dy}{dx},x=y^{3}-8y^{2}+5,(-2,1)
inverse oflaplace 1/(s^2-2s-3)	inverselaplace\:\frac{1}{s^{2}-2s-3}
limit as x approaches 0+of (x-[x])/([x]-2x)	\lim\:_{x\to\:0+}(\frac{x-[x]}{[x]-2x})
derivative of x^2log_{2}(7-6x)	\frac{d}{dx}(x^{2}\log_{2}(7-6x))
integral of 6sin^2(3x)cos(3x)ln(sin(3x))	\int\:6\sin^{2}(3x)\cos(3x)\ln(\sin(3x))dx
integral from 0 to 4 of 4sqrt(x)-2x	\int\:_{0}^{4}4\sqrt{x}-2xdx
(dy)/(dx)=e^{3x}+9y	\frac{dy}{dx}=e^{3x}+9y
limit as x approaches-2 of (sin(-pix))/(2+x)	\lim\:_{x\to\:-2}(\frac{\sin(-πx)}{2+x})
integral from 2 to 3 of (22)/(sqrt(3-x))	\int\:_{2}^{3}\frac{22}{\sqrt{3-x}}dx
tangent of f(x)=x^3-4x,\at x=0	tangent\:f(x)=x^{3}-4x,\at\:x=0
inverse oflaplace 2/((s+2))	inverselaplace\:\frac{2}{(s+2)}
derivative of ln(((8x-9)^2)/(-x-1))	derivative\:\ln(\frac{(8x-9)^{2}}{-x-1})
derivative of x^{11/2}	derivative\:x^{\frac{11}{2}}
x^'=-x^2	x^{\prime\:}=-x^{2}
derivative of f(2)=3x^2-2x+5	derivative\:f(2)=3x^{2}-2x+5
integral of (x+2)/(x^3)	\int\:\frac{x+2}{x^{3}}dx
(\partial)/(\partial x)(2xe^{x^2})	\frac{\partial\:}{\partial\:x}(2xe^{x^{2}})
integral of (sec^2(pix)-sqrt(x))	\int\:(\sec^{2}(πx)-\sqrt{x})dx
(\partial)/(\partial x)(((yx)/(zw))^{1/2})	\frac{\partial\:}{\partial\:x}((\frac{yx}{zw})^{\frac{1}{2}})
derivative of (4-xe^x/(x+e^x))	\frac{d}{dx}(\frac{4-xe^{x}}{x+e^{x}})
sum from n=1 to infinity of (cos(npi))/(n^2)	\sum\:_{n=1}^{\infty\:}\frac{\cos(nπ)}{n^{2}}
limit as x approaches 2 of (sqrt(x+47-7))/(5x-10)	\lim\:_{x\to\:2}(\frac{\sqrt{x+47-7}}{5x-10})
(\partial)/(\partial x)(y^5sin(6x))	\frac{\partial\:}{\partial\:x}(y^{5}\sin(6x))
integral from 0 to 1 of integral from 0 to s^5 of cos(s^6)	\int\:_{0}^{1}\int\:_{0}^{s^{5}}\cos(s^{6})dtds
y^'=-ty	y^{\prime\:}=-ty
(dy)/(dx)=y(1-y)	\frac{dy}{dx}=y(1-y)
limit as x approaches 4 of 5x^2-2x+3	\lim\:_{x\to\:4}(5x^{2}-2x+3)
limit as x approaches 7 of ((x^2-2x-35))/(x-7)	\lim\:_{x\to\:7}(\frac{(x^{2}-2x-35)}{x-7})
limit as x approaches 0 of (1^x-9^x)/x	\lim\:_{x\to\:0}(\frac{1^{x}-9^{x}}{x})
(\partial)/(\partial x)(x^2+2y^2-x^2y)	\frac{\partial\:}{\partial\:x}(x^{2}+2y^{2}-x^{2}y)
integral of (10)/(sqrt(1-x^2))	\int\:\frac{10}{\sqrt{1-x^{2}}}dx
xy^{''}-2y^'=0	xy^{\prime\:\prime\:}-2y^{\prime\:}=0
integral of 6/((9t^2+1)^2)	\int\:\frac{6}{(9t^{2}+1)^{2}}dt
derivative of Ax^2e^x	\frac{d}{dx}(Ax^{2}e^{x})
integral from 0 to 3 of 450.268e^{1.12567t}	\int\:_{0}^{3}450.268e^{1.12567t}dt
integral of (x^2+1)/(x^4+1)	\int\:\frac{x^{2}+1}{x^{4}+1}dx
derivative of 2e^xcos(x)	derivative\:2e^{x}\cos(x)
(\partial)/(\partial x)(ln(x^3))	\frac{\partial\:}{\partial\:x}(\ln(x^{3}))
integral of 1/((1-y))	\int\:\frac{1}{(1-y)}dy
integral of (3/x)	\int\:(\frac{3}{x})dx
(\partial)/(\partial z)(5sin^2(z))	\frac{\partial\:}{\partial\:z}(5\sin^{2}(z))
sum from n=1 to infinity of 4+(-1)^n	\sum\:_{n=1}^{\infty\:}4+(-1)^{n}
integral of 5(tan(x))(ln(cos(x)))	\int\:5(\tan(x))(\ln(\cos(x)))dx
integral from 2 to infinity of 1/(3x+2)	\int\:_{2}^{\infty\:}\frac{1}{3x+2}dx
derivative of 5x+1	derivative\:5x+1
integral of e^xsin(6e^x+3)	\int\:e^{x}\sin(6e^{x}+3)dx
slope of sqrt(sin(cos^2(x))),\at x=pi	slope\:\sqrt{\sin(\cos^{2}(x))},\at\:x=π
derivative of (6+x)/(1-6x)	derivative\:\frac{6+x}{1-6x}
inverse oflaplace 6/(s^2)	inverselaplace\:\frac{6}{s^{2}}

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