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Popular Calculus Problems

f(x)=arcsech(x)	f(x)=\arcsech(x)
integral of sqrt(t)-5cos(t)	\int\:\sqrt{t}-5\cos(t)dt
integral of ((x-2)^3)/((x-2))	\int\:\frac{(x-2)^{3}}{(x-2)}dx
(dy)/(dx)=14x^8	\frac{dy}{dx}=14x^{8}
derivative of x*\|x\|	\frac{d}{dx}(x\cdot\:\left\|x\right\|)
limit as x approaches-1 of x+a	\lim\:_{x\to\:-1}(x+a)
limit as x approaches 2 of 2e^{x-2}	\lim\:_{x\to\:2}(2e^{x-2})
integral of 4/3 x	\int\:\frac{4}{3}xdx
derivative of xe^{-(sqrt(3)x/2})	\frac{d}{dx}(xe^{-\frac{\sqrt{3}x}{2}})
tangent of f(x)=3e^x+2x,\at x=0	tangent\:f(x)=3e^{x}+2x,\at\:x=0
integral of (2x)/((2-x)^6)	\int\:\frac{2x}{(2-x)^{6}}dx
derivative of 9pix^2	derivative\:9πx^{2}
integral of 1/(1+81x^2)	\int\:\frac{1}{1+81x^{2}}dx
(2xsin(y)cos(y))y^'=4x^2+sin^2(y)	(2x\sin(y)\cos(y))y^{\prime\:}=4x^{2}+\sin^{2}(y)
derivative of tan(e^{6x}+e^{tan(6x)})	\frac{d}{dx}(\tan(e^{6x})+e^{\tan(6x)})
(\partial)/(\partial y)(e^xsin(2y))	\frac{\partial\:}{\partial\:y}(e^{x}\sin(2y))
integral of (14x^{13})	\int\:(14x^{13})dx
(\partial)/(\partial x)(xe^x+2ye^x)	\frac{\partial\:}{\partial\:x}(xe^{x}+2ye^{x})
derivative of (e^x(x-2))/((x-1)^2)	derivative\:\frac{e^{x}(x-2)}{(x-1)^{2}}
integral of 1/(x^2+9x+18)	\int\:\frac{1}{x^{2}+9x+18}dx
integral of sqrt(sin(θ)+1)	\int\:\sqrt{\sin(θ)+1}dθ
integral of cosh(5x)	\int\:\cosh(5x)dx
taylor x,1	taylor\:x,1
integral from 7 to 11 of 2/(x^3)	\int\:_{7}^{11}\frac{2}{x^{3}}dx
(\partial)/(\partial y)((9x-4y)(12x+2y))	\frac{\partial\:}{\partial\:y}((9x-4y)(12x+2y))
derivative of 8a^6-14a^3-15	derivative\:8a^{6}-14a^{3}-15
integral from 1 to 3 of (x+1)/(x(x^2+1))	\int\:_{1}^{3}\frac{x+1}{x(x^{2}+1)}dx
tangent of f(x)=2x^2-x^4,(1,1)	tangent\:f(x)=2x^{2}-x^{4},(1,1)
integral from 1 to 8 of (ln(x))/(x^2)	\int\:_{1}^{8}\frac{\ln(x)}{x^{2}}dx
sum from n=1 to infinity of 6/(n(n+1))	\sum\:_{n=1}^{\infty\:}\frac{6}{n(n+1)}
derivative of x/2+cos(x)	\frac{d}{dx}(\frac{x}{2}+\cos(x))
ydy-xdx=0	ydy-xdx=0
(y-yx^2)y^'=(y+1)^2	(y-yx^{2})y^{\prime\:}=(y+1)^{2}
derivative of ycos(xy)	\frac{d}{dx}(y\cos(xy))
area 5x^2,x^2+4	area\:5x^{2},x^{2}+4
x^2y^'+xy=8	x^{2}y^{\prime\:}+xy=8
(\partial)/(\partial x)(4xy+3)	\frac{\partial\:}{\partial\:x}(4xy+3)
integral of xcos((pix)/2)	\int\:x\cos(\frac{πx}{2})dx
integral from 1 to 2 of 1/(2x+1)	\int\:_{1}^{2}\frac{1}{2x+1}dx
integral of v(1-2/3 v^2)^6	\int\:v(1-\frac{2}{3}v^{2})^{6}dv
(\partial)/(\partial x)(4ycos(-6x))	\frac{\partial\:}{\partial\:x}(4y\cos(-6x))
derivative of 1/(x-7)	\frac{d}{dx}(\frac{1}{x-7})
integral of 1/x e^x	\int\:\frac{1}{x}e^{x}dx
derivative of f(x)=(4x^2+6x+6)/(sqrt(x))	derivative\:f(x)=\frac{4x^{2}+6x+6}{\sqrt{x}}
integral of e^{-2x}cos(4x)	\int\:e^{-2x}\cos(4x)dx
integral of 1/(sqrt(48x+6x^2))	\int\:\frac{1}{\sqrt{48x+6x^{2}}}dx
limit as x approaches 6 of 8x^2-7x+1	\lim\:_{x\to\:6}(8x^{2}-7x+1)
derivative of 3cos(-x^3+3x+1)	\frac{d}{dx}(3\cos(-x^{3}+3x+1))
integral of x-(5-sqrt(25-4x))/2	\int\:x-\frac{5-\sqrt{25-4x}}{2}dx
integral of 1/(n+3)	\int\:\frac{1}{n+3}
limit as x approaches 0 of (ln(1-x))/x	\lim\:_{x\to\:0}(\frac{\ln(1-x)}{x})
derivative of 23	\frac{d}{dx}(23)
area x=4-(y-2)^2,y=x	area\:x=4-(y-2)^{2},y=x
integral of 3x-1/x-7e^x+14e	\int\:3x-\frac{1}{x}-7e^{x}+14edx
tangent of 5/x ,\at x=2	tangent\:\frac{5}{x},\at\:x=2
integral from 0 to 9 of (10)/((1+x)^2)	\int\:_{0}^{9}\frac{10}{(1+x)^{2}}dx
limit as x approaches-3 of ln(x+3)	\lim\:_{x\to\:-3}(\ln(x+3))
integral of t/(e^{2t)}	\int\:\frac{t}{e^{2t}}dt
integral from-2 to 9 of f(x)	\int\:_{-2}^{9}f(x)dx
(\partial)/(\partial y)(2xy^3+3)	\frac{\partial\:}{\partial\:y}(2xy^{3}+3)
tangent of 4/(x+2)	tangent\:\frac{4}{x+2}
integral of (4t^3-3t^2+4t)/(t^2+1)	\int\:\frac{4t^{3}-3t^{2}+4t}{t^{2}+1}dt
integral of (4x)/((x^2+4)^2)	\int\:\frac{4x}{(x^{2}+4)^{2}}dx
(\partial)/(\partial x)(xe^y+ye^x)	\frac{\partial\:}{\partial\:x}(xe^{y}+ye^{x})
integral from 0 to 1 of (49)/(x^5)	\int\:_{0}^{1}\frac{49}{x^{5}}dx
tangent of 7sqrt(x),\at x=4	tangent\:7\sqrt{x},\at\:x=4
integral of 8u^{9/8}	\int\:8u^{\frac{9}{8}}du
area x=y^2-2,(-2,2)	area\:x=y^{2}-2,(-2,2)
y'=y(1-0.0008y)	y\prime\:=y(1-0.0008y)
derivative of f(x)=(2x)/(x-1)	derivative\:f(x)=\frac{2x}{x-1}
integral of sin(x)*cos^2(x)	\int\:\sin(x)\cdot\:\cos^{2}(x)dx
derivative of e^{4x^{2+1}}	\frac{d}{dx}(e^{4x^{2+1}})
limit as x approaches 0+of 2/x-3/2	\lim\:_{x\to\:0+}(\frac{2}{x}-\frac{3}{2})
integral of cos(x)(3+8sin^2(x))	\int\:\cos(x)(3+8\sin^{2}(x))dx
limit as x approaches 3+of (3x+2)/(x-3)	\lim\:_{x\to\:3+}(\frac{3x+2}{x-3})
derivative of-e^xsin(x)	\frac{d}{dx}(-e^{x}\sin(x))
integral of (e^{2x}-e^{-2x})	\int\:(e^{2x}-e^{-2x})dx
integral of 100-x^2	\int\:100-x^{2}dx
integral from-1 to 1 of 4	\int\:_{-1}^{1}4dx
(\partial)/(\partial x)(ln(6x^2+7y^2+7))	\frac{\partial\:}{\partial\:x}(\ln(6x^{2}+7y^{2}+7))
(dy)/(dx)+tan(x)y=cos^2(x)	\frac{dy}{dx}+\tan(x)y=\cos^{2}(x)
limit as x approaches infinity of x/2	\lim\:_{x\to\:\infty\:}(\frac{x}{2})
derivative of x^2*sin(1/x)	\frac{d}{dx}(x^{2}\cdot\:\sin(\frac{1}{x}))
sum from n=1 to infinity of 3/(2n+3)	\sum\:_{n=1}^{\infty\:}\frac{3}{2n+3}
integral of (5e^{-0.4x})	\int\:(5e^{-0.4x})dx
taylor e^{-2x}	taylor\:e^{-2x}
integral of 6sec^2(3x)tan(3x)	\int\:6\sec^{2}(3x)\tan(3x)dx
integral from 4 to 9 of ((sqrt(x)+3)^2)/(2sqrt(x))	\int\:_{4}^{9}\frac{(\sqrt{x}+3)^{2}}{2\sqrt{x}}dx
integral of ln(x)e^x	\int\:\ln(x)e^{x}dx
integral of (3-x)/(x^2+1)	\int\:\frac{3-x}{x^{2}+1}dx
(\partial)/(\partial x)((5xy^2)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{5xy^{2}}{x^{2}+y^{2}})
derivative of x^23^x	\frac{d}{dx}(x^{2}3^{x})
integral of x/((x+2)(x^2+1))	\int\:\frac{x}{(x+2)(x^{2}+1)}dx
derivative of y=f(x)=cos(3x^2)	derivative\:y=f(x)=\cos(3x^{2})
6y^{''}-y^'-y=0,y(0)=10,y^'(0)=0	6y^{\prime\:\prime\:}-y^{\prime\:}-y=0,y(0)=10,y^{\prime\:}(0)=0
limit as x approaches 2.1 of-x^2+5x-2	\lim\:_{x\to\:2.1}(-x^{2}+5x-2)
integral of ((x^2-2x+1))/((x^2+x))	\int\:\frac{(x^{2}-2x+1)}{(x^{2}+x)}dx
derivative of 1/(a-x)	\frac{d}{dx}(\frac{1}{a-x})
(\partial)/(\partial x)(-0.06x^2+1.08x)	\frac{\partial\:}{\partial\:x}(-0.06x^{2}+1.08x)
derivative of 2x^3-x^2+2	derivative\:2x^{3}-x^{2}+2

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