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Popular Calculus Problems

f(x)=ln(1+2x)	f(x)=\ln(1+2x)
d/(dt)(1/(t+1))	\frac{d}{dt}(\frac{1}{t+1})
y-y^'(x-10)=x	y-y^{\prime\:}(x-10)=x
integral from 0 to pi/3 of tan^2(x)	\int\:_{0}^{\frac{π}{3}}\tan^{2}(x)dx
tangent of y=2x^3-x^2+2,(1,3)	tangent\:y=2x^{3}-x^{2}+2,(1,3)
integral of 1-4x^2	\int\:1-4x^{2}dx
limit as x approaches 0 of 1/x-1/(x^2+1)	\lim\:_{x\to\:0}(\frac{1}{x}-\frac{1}{x^{2}+1})
integral of 1/(sqrt(1-25x^2))	\int\:\frac{1}{\sqrt{1-25x^{2}}}dx
tangent of f(x)=(x^3+x^2+6)/x ,\at x=1	tangent\:f(x)=\frac{x^{3}+x^{2}+6}{x},\at\:x=1
(\partial)/(\partial x)(3x^4y^8+7x^5y^6)	\frac{\partial\:}{\partial\:x}(3x^{4}y^{8}+7x^{5}y^{6})
integral of 7(1+tan^2(a))	\int\:7(1+\tan^{2}(a))da
derivative of h(x)= 8/x-2/(x^3)+1/(x^4)	derivative\:h(x)=\frac{8}{x}-\frac{2}{x^{3}}+\frac{1}{x^{4}}
y^{''}-14y^'+85y=0	y^{\prime\:\prime\:}-14y^{\prime\:}+85y=0
(\partial)/(\partial x)(4/x)	\frac{\partial\:}{\partial\:x}(\frac{4}{x})
derivative of-(12)/(s^5)	derivative\:-\frac{12}{s^{5}}
inverse oflaplace 2/(s^4)	inverselaplace\:\frac{2}{s^{4}}
integral of 2/((t+4)(t-1))	\int\:\frac{2}{(t+4)(t-1)}dt
derivative of (-2x/((x^2+1)^2))	\frac{d}{dx}(\frac{-2x}{(x^{2}+1)^{2}})
derivative of ln((x^{4/3}cos(x))/(7x+6))	derivative\:\ln(\frac{x^{\frac{4}{3}}\cos(x)}{7x+6})
y^{''''}+5y^{''}+4y=0	y^{\prime\:\prime\:\prime\:\prime\:}+5y^{\prime\:\prime\:}+4y=0
integral of 1/(a+v^2)	\int\:\frac{1}{a+v^{2}}dv
derivative of 3x^2-18x	\frac{d}{dx}(3x^{2}-18x)
derivative of f(x)=3x^3+2e^x	derivative\:f(x)=3x^{3}+2e^{x}
integral of cot^2(2x)	\int\:\cot^{2}(2x)dx
integral of (4-r^2)^{3/2}	\int\:(4-r^{2})^{\frac{3}{2}}dr
inverse oflaplace 1/(s^2+1)	inverselaplace\:\frac{1}{s^{2}+1}
d/(dt)(2cos(t))	\frac{d}{dt}(2\cos(t))
(\partial)/(\partial z)(ln(z))	\frac{\partial\:}{\partial\:z}(\ln(z))
(\partial)/(\partial x)(2y^7+8y^7x^7)	\frac{\partial\:}{\partial\:x}(2y^{7}+8y^{7}x^{7})
derivative of f(x)=cos(x)+sin(x)	derivative\:f(x)=\cos(x)+\sin(x)
(dx)/(dy)=4(x^2+1),x(pi/4)=1	\frac{dx}{dy}=4(x^{2}+1),x(\frac{π}{4})=1
t((dy)/(dt))=t^3+22t^3y	t(\frac{dy}{dt})=t^{3}+22t^{3}y
integral of (1+cos(θ))^2	\int\:(1+\cos(θ))^{2}dθ
area y= 1/x ,y=x,y= 1/4 x	area\:y=\frac{1}{x},y=x,y=\frac{1}{4}x
integral from 1 to 6 of (x^2+5)/(7x-x^2)	\int\:_{1}^{6}\frac{x^{2}+5}{7x-x^{2}}dx
laplacetransform (cos(7t))/(e^{5t)}	laplacetransform\:\frac{\cos(7t)}{e^{5t}}
x(dy)/(dx)+y=y^2x^2ln(x)	x\frac{dy}{dx}+y=y^{2}x^{2}\ln(x)
integral of y/(x^2+y^2)	\int\:\frac{y}{x^{2}+y^{2}}dx
inverse oflaplace (2s+12)/((s^2+2s+5))	inverselaplace\:\frac{2s+12}{(s^{2}+2s+5)}
(dx)/(dt)=sin(t)	\frac{dx}{dt}=\sin(t)
limit as x approaches infinity of 5-x	\lim\:_{x\to\:\infty\:}(5-x)
derivative of sin^2(pix)	\frac{d}{dx}(\sin^{2}(πx))
integral of x^{-8}	\int\:x^{-8}dx
tangent of y= x/(1+x^2),\at x=0	tangent\:y=\frac{x}{1+x^{2}},\at\:x=0
(dy)/(dt)=3y-1	\frac{dy}{dt}=3y-1
taylor e^x*sin(x)	taylor\:e^{x}\cdot\:\sin(x)
limit as x approaches 2 of-16x^2+76x	\lim\:_{x\to\:2}(-16x^{2}+76x)
longdivision ((x^5-5))/((x+1))	longdivision\:\frac{(x^{5}-5)}{(x+1)}
integral of 1/((1-y)^2)	\int\:\frac{1}{(1-y)^{2}}dy
derivative of xln(5)	\frac{d}{dx}(x\ln(5))
y^'(x-1)-2+3x+y=0	y^{\prime\:}(x-1)-2+3x+y=0
y^{''}+8y^'+19y=0,y(0)=1,y^'(0)=2	y^{\prime\:\prime\:}+8y^{\prime\:}+19y=0,y(0)=1,y^{\prime\:}(0)=2
integral of sin^{10}(7x)cos^3(7x)	\int\:\sin^{10}(7x)\cos^{3}(7x)dx
limit as x approaches 0+of 3^{1/x}	\lim\:_{x\to\:0+}(3^{\frac{1}{x}})
integral of 2x\sqrt[3]{1+x^2}	\int\:2x\sqrt[3]{1+x^{2}}dx
2ty'+(4+12t^3-120t^2)y=0	2ty\prime\:+(4+12t^{3}-120t^{2})y=0
inverse oflaplace (6s+3)/(s^2)	inverselaplace\:\frac{6s+3}{s^{2}}
integral of x/((x^2-7x+12))	\int\:\frac{x}{(x^{2}-7x+12)}dx
sum from n=0 to infinity of (x/2-3)^n	\sum\:_{n=0}^{\infty\:}(\frac{x}{2}-3)^{n}
derivative of (2{r}(xa^{{r}(x)x}+n)^{{p}(x)})	\frac{d}{dx}((2{r}(x)a^{{r}(x)x}+n)^{{p}(x)})
y^'=((-y^2))/(-(xy-x^3))	y^{\prime\:}=\frac{(-y^{2})}{-(xy-x^{3})}
(\partial)/(\partial y)(7sin(xy))	\frac{\partial\:}{\partial\:y}(7\sin(xy))
(\partial)/(\partial x)(3xe^{5xy})	\frac{\partial\:}{\partial\:x}(3xe^{5xy})
limit as x approaches-4 of x	\lim\:_{x\to\:-4}(x)
integral of (x^2)/((1+2x)^{1/3)}	\int\:\frac{x^{2}}{(1+2x)^{\frac{1}{3}}}dx
(\partial)/(\partial y)(e^{xy}y^2+x/y)	\frac{\partial\:}{\partial\:y}(e^{xy}y^{2}+\frac{x}{y})
(\partial)/(\partial r)(sqrt(r^2+s^2))	\frac{\partial\:}{\partial\:r}(\sqrt{r^{2}+s^{2}})
derivative of sqrt(sin(\sqrt{x)})	\frac{d}{dx}(\sqrt{\sin(\sqrt{x})})
derivative of x^2ln(x^3+2x-1)	\frac{d}{dx}(x^{2}\ln(x^{3}+2x-1))
derivative of y=(7-3x^3)^3	derivative\:y=(7-3x^{3})^{3}
integral of 16e^x	\int\:16e^{x}dx
derivative of (f(x))/(x^2+8)	derivative\:\frac{f(x)}{x^{2}+8}
(dx)/(dt)=0.3*10-x/(40)	\frac{dx}{dt}=0.3\cdot\:10-\frac{x}{40}
derivative of csc^2(θ)-4	derivative\:\csc^{2}(θ)-4
integral of 1/(3+sin^2(x)-cos^2(x))	\int\:\frac{1}{3+\sin^{2}(x)-\cos^{2}(x)}dx
derivative of h(x)= 1/(x^2+4x-21)	derivative\:h(x)=\frac{1}{x^{2}+4x-21}
integral of (sqrt(x)+1/(x^4))	\int\:(\sqrt{x}+\frac{1}{x^{4}})dx
derivative of 19	\frac{d}{dx}(19)
integral of ln((x+2)/(x+1))	\int\:\ln(\frac{x+2}{x+1})dx
area 7x,x*sqrt((15^2-x^2))	area\:7x,x\cdot\:\sqrt{(15^{2}-x^{2})}
derivative of e^{x^3+8x}	\frac{d}{dx}(e^{x^{3}+8x})
derivative of 2sqrt(1+sin(2t))	derivative\:2\sqrt{1+\sin(2t)}
integral of (x+1)sqrt(8x+9)	\int\:(x+1)\sqrt{8x+9}dx
taylor (2x)/((1+x^2)^2)	taylor\:\frac{2x}{(1+x^{2})^{2}}
derivative of x^3+5x+7	\frac{d}{dx}(x^{3}+5x+7)
laplacetransform e^{-t}+2e^{-2t}+te^{-3t}	laplacetransform\:e^{-t}+2e^{-2t}+te^{-3t}
integral of (5cosh(sqrt(x)))/(sqrt(x))	\int\:\frac{5\cosh(\sqrt{x})}{\sqrt{x}}dx
sum from n=0 to infinity of n/(2n^2+1)	\sum\:_{n=0}^{\infty\:}\frac{n}{2n^{2}+1}
limit as x approaches 4 of 7/(x-5)	\lim\:_{x\to\:4}(\frac{7}{x-5})
derivative of (x^2-5x+8(3x^2-2))	\frac{d}{dx}((x^{2}-5x+8)(3x^{2}-2))
integral of (5x^2+7)/(x 4/3)	\int\:\frac{5x^{2}+7}{x\frac{4}{3}}dx
limit as x approaches 0 of sin(pi/2-x)	\lim\:_{x\to\:0}(\sin(\frac{π}{2}-x))
derivative of log_{ln(x}(e))	\frac{d}{dx}(\log_{\ln(x)}(e))
integral of 3/x	\int\:\frac{3}{x}dx
limit as x approaches 0 of (x^3-1)/(x-1)	\lim\:_{x\to\:0}(\frac{x^{3}-1}{x-1})
area x=y^2,x=36-y^2	area\:x=y^{2},x=36-y^{2}
derivative of y= x/8-8/x	derivative\:y=\frac{x}{8}-\frac{8}{x}
integral from t to 1 of 1/(sqrt(x-1))	\int\:_{t}^{1}\frac{1}{\sqrt{x-1}}dx
derivative of (x-2/(x+3))	\frac{d}{dx}(\frac{x-2}{x+3})
(\partial)/(\partial x)(2xcos(x+2y))	\frac{\partial\:}{\partial\:x}(2x\cos(x+2y))

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