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Popular Calculus Problems

integral from 1 to 5 of 4/(x^2)	\int\:_{1}^{5}\frac{4}{x^{2}}dx
d/(dy)(arctan(y))	\frac{d}{dy}(\arctan(y))
integral of tan(g)(x)	\int\:\tan(g)(x)dx
integral of cosh(t)	\int\:\cosh(t)dt
derivative of (x+5)/(x+1)	derivative\:\frac{x+5}{x+1}
integral of 8x^3+5	\int\:8x^{3}+5dx
y^'+1/2 y=8	y^{\prime\:}+\frac{1}{2}y=8
integral of (3x^2-2)/((x^3-2x)^7)	\int\:\frac{3x^{2}-2}{(x^{3}-2x)^{7}}dx
integral of x^{-p}	\int\:x^{-p}dx
(\partial)/(\partial x)(6x^7y^5z^6)	\frac{\partial\:}{\partial\:x}(6x^{7}y^{5}z^{6})
integral of e^{-st}t^4	\int\:e^{-st}t^{4}dt
integral of sqrt(1-x^2)x	\int\:\sqrt{1-x^{2}}xdx
area \|20x+x^2-x^3\|,y=0,[-4,5]	area\:\left\|20x+x^{2}-x^{3}\right\|,y=0,[-4,5]
area x^2+4x-5,-x^2+4x+3	area\:x^{2}+4x-5,-x^{2}+4x+3
limit as x approaches 1 of 4x^2	\lim\:_{x\to\:1}(4x^{2})
integral of 1/((sin(4x))^2)	\int\:\frac{1}{(\sin(4x))^{2}}dx
derivative of-(2(-3x^2+1)/((1+x^2)^3))	\frac{d}{dx}(-\frac{2(-3x^{2}+1)}{(1+x^{2})^{3}})
tangent of sqrt((x^4-x+1)/(x^4+x+1))	tangent\:\sqrt{\frac{x^{4}-x+1}{x^{4}+x+1}}
(\partial)/(\partial y)(x^2+xy+3x+2y+5)	\frac{\partial\:}{\partial\:y}(x^{2}+xy+3x+2y+5)
derivative of 1/(x^2+16)	\frac{d}{dx}(\frac{1}{x^{2}+16})
integral from 0 to 4 of sqrt(4x+9)	\int\:_{0}^{4}\sqrt{4x+9}dx
integral from-9 to 9 of 81-x^2	\int\:_{-9}^{9}81-x^{2}dx
laplacetransform 4t^2-3cos(2t)+5e^{-t}	laplacetransform\:4t^{2}-3\cos(2t)+5e^{-t}
area x-1,sqrt(x-1)	area\:x-1,\sqrt{x-1}
derivative of sqrt(\|x\|)	\frac{d}{dx}(\sqrt{\left\|x\right\|})
integral from 1 to 2 of (3x-2)^2	\int\:_{1}^{2}(3x-2)^{2}dx
xy^'+y=-9xy^2,y(1)=-4	xy^{\prime\:}+y=-9xy^{2},y(1)=-4
integral from 0 to pi/5 of sin^4(5x)	\int\:_{0}^{\frac{π}{5}}\sin^{4}(5x)dx
y^'+y= 1/(1+t^2)	y^{\prime\:}+y=\frac{1}{1+t^{2}}
limit as x approaches 0 of x^2ln(4x^2)	\lim\:_{x\to\:0}(x^{2}\ln(4x^{2}))
derivative of 1/(4s^3)	derivative\:\frac{1}{4s^{3}}
(\partial)/(\partial x)(1-x^2-x-3y^2+y)	\frac{\partial\:}{\partial\:x}(1-x^{2}-x-3y^{2}+y)
(\partial)/(\partial x)(xy-4x^2y)	\frac{\partial\:}{\partial\:x}(xy-4x^{2}y)
y^'=4y+x^2+9	y^{\prime\:}=4y+x^{2}+9
integral of (3^x-sec^2(x))	\int\:(3^{x}-\sec^{2}(x))dx
(dy)/(dx)=-4x+6x^2	\frac{dy}{dx}=-4x+6x^{2}
limit as x approaches 4 of x^2+1	\lim\:_{x\to\:4}(x^{2}+1)
derivative of sqrt(e^x)	derivative\:\sqrt{e^{x}}
derivative of f(x)=(x^3)/6+1/(2x)	derivative\:f(x)=\frac{x^{3}}{6}+\frac{1}{2x}
derivative of (1+cos(x)/(sin(x)))	\frac{d}{dx}(\frac{1+\cos(x)}{\sin(x)})
(\partial)/(\partial x)(3x-sqrt(3y^2+z^2))	\frac{\partial\:}{\partial\:x}(3x-\sqrt{3y^{2}+z^{2}})
integral of (x-e^{-x})^2	\int\:(x-e^{-x})^{2}dx
tangent of f(x)=(x^2)/(x-7)	tangent\:f(x)=\frac{x^{2}}{x-7}
derivative of 5x-6	\frac{d}{dx}(5x-6)
integral of (x+15)/(x^2+16x+68)	\int\:\frac{x+15}{x^{2}+16x+68}dx
integral of xsec^3(x^2)	\int\:x\sec^{3}(x^{2})dx
derivative of (4x-6/(x-6))	\frac{d}{dx}(\frac{4x-6}{x-6})
derivative of 1/2 x^2e^xln(x)	\frac{d}{dx}(\frac{1}{2}x^{2}e^{x}\ln(x))
derivative of f(x)=(cos(e^x))/(x^4+1)	derivative\:f(x)=\frac{\cos(e^{x})}{x^{4}+1}
area 2sqrt(x),(2x)/3	area\:2\sqrt{x},\frac{2x}{3}
integral of (x^2+1)/(xsqrt(1+x^4))	\int\:\frac{x^{2}+1}{x\sqrt{1+x^{4}}}dx
d/(dt)(e^{2t}cos(2t))	\frac{d}{dt}(e^{2t}\cos(2t))
derivative of 8x^4ln(6x)	derivative\:8x^{4}\ln(6x)
integral of cot(x)cos^2(x)	\int\:\cot(x)\cos^{2}(x)dx
derivative of (x^2-1^4)	\frac{d}{dx}((x^{2}-1)^{4})
integral of (x^2+4)/((x-5)(x^2+9))	\int\:\frac{x^{2}+4}{(x-5)(x^{2}+9)}dx
limit as x approaches 0 of ln(x)*x	\lim\:_{x\to\:0}(\ln(x)\cdot\:x)
integral of (x^2+1)/((x-4)(x-3)^2)	\int\:\frac{x^{2}+1}{(x-4)(x-3)^{2}}dx
integral of (x/3)^n	\int\:(\frac{x}{3})^{n}dx
derivative of (x^4-3)^3(x^2+6)^5	derivative\:(x^{4}-3)^{3}(x^{2}+6)^{5}
derivative of 4x^{5/4}+2x^{3/2}+5x	\frac{d}{dx}(4x^{\frac{5}{4}}+2x^{\frac{3}{2}}+5x)
derivative of 15000e^{-0.6x}	derivative\:15000e^{-0.6x}
limit as x approaches 2-of 5x^3-2/(x-2)	\lim\:_{x\to\:2-}(5x^{3}-\frac{2}{x-2})
derivative of 9	derivative\:9
integral from-6 to 6 of 1/v	\int\:_{-6}^{6}\frac{1}{v}dv
derivative of y=ln(sqrt(2^3))	derivative\:y=\ln(\sqrt{2^{3}})
derivative of (x^2/(sin(x)))	\frac{d}{dx}(\frac{x^{2}}{\sin(x)})
sum from n=1 to infinity of (3n)x^n	\sum\:_{n=1}^{\infty\:}(3n)x^{n}
(\partial)/(\partial x)(9xy^2)	\frac{\partial\:}{\partial\:x}(9xy^{2})
integral from 0 to 2 of (1-2x)	\int\:_{0}^{2}(1-2x)dx
integral of (2x^3+x^2+8x-12)/(x^3+4x)	\int\:\frac{2x^{3}+x^{2}+8x-12}{x^{3}+4x}dx
slope of (0)(1.2)	slope\:(0)(1.2)
laplacetransform 35t^2	laplacetransform\:35t^{2}
(dy)/(dx)=(4(1-y)^2)/((1-2x)^2)	\frac{dy}{dx}=\frac{4(1-y)^{2}}{(1-2x)^{2}}
derivative of sqrt(1+1/(x^2))	\frac{d}{dx}(\sqrt{1+\frac{1}{x^{2}}})
derivative of-6sin(2x)	\frac{d}{dx}(-6\sin(2x))
derivative of (sqrt(81+x^2)/3+(15-x)/5)	\frac{d}{dx}(\frac{\sqrt{81+x^{2}}}{3}+\frac{15-x}{5})
derivative of-sin(xy)	\frac{d}{dx}(-\sin(x)y)
(\partial)/(\partial x)(-5ycos(-9x))	\frac{\partial\:}{\partial\:x}(-5y\cos(-9x))
limit as x approaches infinity of 7-e^x	\lim\:_{x\to\:\infty\:}(7-e^{x})
integral from 0 to 1 of (16x)/(8x^2+2)	\int\:_{0}^{1}\frac{16x}{8x^{2}+2}dx
integral of tan^3(x)sec^{-1/2}(x)	\int\:\tan^{3}(x)\sec^{-\frac{1}{2}}(x)dx
(\partial)/(\partial t)(sin(t))	\frac{\partial\:}{\partial\:t}(\sin(t))
x^2ln(x/y)dy+xydx=0	x^{2}\ln(\frac{x}{y})dy+xydx=0
(\partial)/(\partial x)(sin(xe^{xy}))	\frac{\partial\:}{\partial\:x}(\sin(xe^{xy}))
y^{''}-y^'+1/4 y=2+e^{x/2}	y^{\prime\:\prime\:}-y^{\prime\:}+\frac{1}{4}y=2+e^{\frac{x}{2}}
integral of (3-x)/(x^3+4x^2+3x)	\int\:\frac{3-x}{x^{3}+4x^{2}+3x}dx
derivative of 4ln(cos(x))	\frac{d}{dx}(4\ln(\cos(x)))
limit as x approaches 3-of 2x-1	\lim\:_{x\to\:3-}(2x-1)
integral from 1 to 4 of 5sqrt(t)ln(t)	\int\:_{1}^{4}5\sqrt{t}\ln(t)dt
limit as x approaches-3 of-5/((x+3)^2)	\lim\:_{x\to\:-3}(-\frac{5}{(x+3)^{2}})
derivative of (8-xe^x/(x+e^x))	\frac{d}{dx}(\frac{8-xe^{x}}{x+e^{x}})
4y^'=(4xy+8x^2+2y^2)/(x^2)	4y^{\prime\:}=\frac{4xy+8x^{2}+2y^{2}}{x^{2}}
y^'+csc(y)=0	y^{\prime\:}+\csc(y)=0
integral of (e^{3x}+1)/(e^x+1)	\int\:\frac{e^{3x}+1}{e^{x}+1}dx
limit as x approaches 3 of 2x^3-4x-10	\lim\:_{x\to\:3}(2x^{3}-4x-10)
derivative of 9x^2sqrt(x)+7x^2	derivative\:9x^{2}\sqrt{x}+7x^{2}
slope of (-9,-2),(3,-1)	slope\:(-9,-2),(3,-1)
integral of (2x+1)(x^2+x)	\int\:(2x+1)(x^{2}+x)dx
inverse oflaplace (-1)/(s(s-2))	inverselaplace\:\frac{-1}{s(s-2)}

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