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Popular Calculus Problems

integral of x^3sqrt((1+9x^4))	\int\:x^{3}\sqrt{(1+9x^{4})}dx
derivative of 1-cos(2x+2cos^2(x))	\frac{d}{dx}(1-\cos(2x)+2\cos^{2}(x))
integral of 6x^{13}e^{-x^7}	\int\:6x^{13}e^{-x^{7}}dx
limit as x approaches 0 of 4/(1+2^{1/x)}	\lim\:_{x\to\:0}(\frac{4}{1+2^{\frac{1}{x}}})
derivative of 4cos(4x)	\frac{d}{dx}(4\cos(4x))
f^'(x)=3x-4,f(-1)= 13/2	f^{\prime\:}(x)=3x-4,f(-1)=\frac{13}{2}
derivative of ln(196sin^2(x))	derivative\:\ln(196\sin^{2}(x))
integral of 1/(5-7x)	\int\:\frac{1}{5-7x}dx
y^{''''}+4y^{''}+4y=0	y^{\prime\:\prime\:\prime\:\prime\:}+4y^{\prime\:\prime\:}+4y=0
(\partial)/(\partial x)(2xy^2-2x^3y)	\frac{\partial\:}{\partial\:x}(2xy^{2}-2x^{3}y)
sum from n=0 to infinity of (((1)^n))/n	\sum\:_{n=0}^{\infty\:}\frac{((1)^{n})}{n}
derivative of y=(x^2+1)/(2x^2-1)	derivative\:y=\frac{x^{2}+1}{2x^{2}-1}
derivative of 1-cos(x-1)	\frac{d}{dx}(1-\cos(x-1))
integral of (e^{sqrt(5x)})/(sqrt(5x))	\int\:\frac{e^{\sqrt{5x}}}{\sqrt{5x}}dx
tangent of f(x)=12sqrt(x)-2x,\at x=9	tangent\:f(x)=12\sqrt{x}-2x,\at\:x=9
integral of 3/(9+x^2)	\int\:\frac{3}{9+x^{2}}dx
maclaurin e^{sin(2x)}	maclaurin\:e^{\sin(2x)}
integral of-2cos(x)+3x^2-5x+4	\int\:-2\cos(x)+3x^{2}-5x+4dx
integral of 3x+1/(3x)	\int\:3x+\frac{1}{3x}dx
y^{''}-6y^'+7y=0,y(0)=0,y^'(0)=7	y^{\prime\:\prime\:}-6y^{\prime\:}+7y=0,y(0)=0,y^{\prime\:}(0)=7
d/(d{x)}({x}e^{({y})/({z)}})	\frac{d}{d{x}}({x}e^{\frac{{y}}{{z}}})
derivative of 7x-6sqrt(x)	derivative\:7x-6\sqrt{x}
integral from 1 to 5 of (ln(x))/(x^2)	\int\:_{1}^{5}\frac{\ln(x)}{x^{2}}dx
derivative of 3x^4-8x^3+6x^2	\frac{d}{dx}(3x^{4}-8x^{3}+6x^{2})
tangent of y=x^4+5e^x	tangent\:y=x^{4}+5e^{x}
derivative of 3e^{3e^x+x}	derivative\:3e^{3e^{x}+x}
integral of (e-x-e^3)(ex+e-5)	\int\:(e-x-e^{3})(ex+e-5)dx
integral from 9 to x of sqrt(1+9t)	\int\:_{9}^{x}\sqrt{1+9t}dt
integral of sec^4(3x)tan^2(3x)	\int\:\sec^{4}(3x)\tan^{2}(3x)dx
derivative of log_{e}(x^3)	\frac{d}{dx}(\log_{e}(x^{3}))
integral from 0 to 2 of 1/8 (x+y)	\int\:_{0}^{2}\frac{1}{8}(x+y)dy
f(x)=e^{2x}-1	f(x)=e^{2x}-1
integral of 5cos^5(x)sin^4(x)	\int\:5\cos^{5}(x)\sin^{4}(x)dx
tangent of y=x^3-2x^2+5,\at x=2	tangent\:y=x^{3}-2x^{2}+5,\at\:x=2
derivative of ln(pi)	derivative\:\ln(π)
limit as x approaches-0.1 of (sin(x))/x	\lim\:_{x\to\:-0.1}(\frac{\sin(x)}{x})
sum from n=1 to infinity of 1/(7+e^{-n)}	\sum\:_{n=1}^{\infty\:}\frac{1}{7+e^{-n}}
limit as n approaches infinity of 3^n7^{-n}	\lim\:_{n\to\:\infty\:}(3^{n}7^{-n})
limit as x approaches 9-of x^2+5x+7	\lim\:_{x\to\:9-}(x^{2}+5x+7)
y^{''}+12y^'+36=0,y(1)=0,y^'(1)=1	y^{\prime\:\prime\:}+12y^{\prime\:}+36=0,y(1)=0,y^{\prime\:}(1)=1
y^'+y=(x+1)^2	y^{\prime\:}+y=(x+1)^{2}
integral of (10)/(x^2+1)	\int\:\frac{10}{x^{2}+1}dx
integral of (x^2)/((x+6)^3)	\int\:\frac{x^{2}}{(x+6)^{3}}dx
d/(dy)(sqrt(17-x^2-4y^2))	\frac{d}{dy}(\sqrt{17-x^{2}-4y^{2}})
integral of (e^x-2/(sqrt(x)))	\int\:(e^{x}-\frac{2}{\sqrt{x}})dx
(\partial)/(\partial x)(sin(x+xy+z^2))	\frac{\partial\:}{\partial\:x}(\sin(x+xy+z^{2}))
(\partial)/(\partial x)(y^4cos(5x))	\frac{\partial\:}{\partial\:x}(y^{4}\cos(5x))
integral from 5 to 8 of 1/(9+(x-5)^2)	\int\:_{5}^{8}\frac{1}{9+(x-5)^{2}}dx
sum from n=1 to infinity}2^{n+1 of-2^n	\sum\:_{n=1}^{\infty\:}2^{n+1}-2^{n}
sum from n=0 to infinity of (sin(8))^n	\sum\:_{n=0}^{\infty\:}(\sin(8))^{n}
derivative of ((4x-2^4)/((-5x+1)^5))	\frac{d}{dx}(\frac{(4x-2)^{4}}{(-5x+1)^{5}})
integral of ((sqrt(x^2-4))/x)	\int\:(\frac{\sqrt{x^{2}-4}}{x})dx
implicit (dy)/(dx),x=y^4	implicit\:\frac{dy}{dx},x=y^{4}
y^'-6/x y=x^9y^8	y^{\prime\:}-\frac{6}{x}y=x^{9}y^{8}
integral of-1/(csc(y))	\int\:-\frac{1}{\csc(y)}dy
(dy)/(dx)=(x^3)/(y^2),y(2)=\sqrt[3]{13}	\frac{dy}{dx}=\frac{x^{3}}{y^{2}},y(2)=\sqrt[3]{13}
derivative of cos^2(ln(x+1)-e^{x^2})	\frac{d}{dx}(\cos^{2}(\ln(x+1))-e^{x^{2}})
derivative of y=5x-1	derivative\:y=5x-1
integral from pi/2 to pi of 2cot(x/3)	\int\:_{\frac{π}{2}}^{π}2\cot(\frac{x}{3})dx
limit as x approaches 1 of (x+1)/(x^3+1)	\lim\:_{x\to\:1}(\frac{x+1}{x^{3}+1})
derivative of 0.1x^3-0.45x^2+2.43x+300	\frac{d}{dx}(0.1x^{3}-0.45x^{2}+2.43x+300)
integral of (sin^5(x))/(cos^4(x))	\int\:\frac{\sin^{5}(x)}{\cos^{4}(x)}dx
limit as t approaches 1+of t^{1/(1-t)}	\lim\:_{t\to\:1+}(t^{\frac{1}{1-t}})
laplacetransform e^{(t-2)}	laplacetransform\:e^{(t-2)}
integral of (3)	\int\:(3)dx
derivative of 1/(x^2+x)	\frac{d}{dx}(\frac{1}{x^{2}+x})
integral of x/(sin^2(2x^2))	\int\:\frac{x}{\sin^{2}(2x^{2})}dx
integral of (sin(x)-7cos(x))	\int\:(\sin(x)-7\cos(x))dx
integral of 2\|x\|	\int\:2\left\|x\right\|dx
integral of (e^x)/(e^{2x)+9}	\int\:\frac{e^{x}}{e^{2x}+9}dx
integral of 7sin^4(xco)s^2x	\int\:7\sin^{4}(xco)s^{2}xdx
limit as x approaches infinity of 1.03^x	\lim\:_{x\to\:\infty\:}(1.03^{x})
y^{''}+pi^2y=0	y^{\prime\:\prime\:}+π^{2}y=0
(\partial)/(\partial x)(cos(x)*sin(y))	\frac{\partial\:}{\partial\:x}(\cos(x)\cdot\:\sin(y))
integral of (cot^4(x))/(csc^2(x))	\int\:\frac{\cot^{4}(x)}{\csc^{2}(x)}dx
f(x)=3sin(2x)	f(x)=3\sin(2x)
(\partial)/(\partial x)(4x^3y+xy^2)	\frac{\partial\:}{\partial\:x}(4x^{3}y+xy^{2})
derivative of-(2x)/((4+x^2)^2)	derivative\:-\frac{2x}{(4+x^{2})^{2}}
tangent of x^3-6x^2-34x+40,\at x=4	tangent\:x^{3}-6x^{2}-34x+40,\at\:x=4
y^{''}-4y^'+13y=0,y(0)=1,y^'(0)=-4	y^{\prime\:\prime\:}-4y^{\prime\:}+13y=0,y(0)=1,y^{\prime\:}(0)=-4
(\partial)/(\partial z)((xy)/(x+y+z))	\frac{\partial\:}{\partial\:z}(\frac{xy}{x+y+z})
derivative of (cos(x)/(4x))	\frac{d}{dx}(\frac{\cos(x)}{4x})
limit as x approaches 1-of x^3-4	\lim\:_{x\to\:1-}(x^{3}-4)
integral of 5-3(1+x^2)^{-1}	\int\:5-3(1+x^{2})^{-1}dx
derivative of y=(arctan(8x))^2	derivative\:y=(\arctan(8x))^{2}
(\partial)/(\partial x)(sqrt(x/(x+y)))	\frac{\partial\:}{\partial\:x}(\sqrt{\frac{x}{x+y}})
integral of (sin(2x))/(sqrt(4-cos^4(x)))	\int\:\frac{\sin(2x)}{\sqrt{4-\cos^{4}(x)}}dx
derivative of ln(x+sqrt(x^2+y^2))	\frac{d}{dx}(\ln(x+\sqrt{x^{2}+y^{2}}))
integral of (x^6)/(x^7-2)	\int\:\frac{x^{6}}{x^{7}-2}dx
integral from 0 to 2 of ((-x+5)-(x^2-9))	\int\:_{0}^{2}((-x+5)-(x^{2}-9))dx
derivative of (2a/(x^3))	\frac{d}{dx}(\frac{2a}{x^{3}})
integral of (12)/((x^2-9))	\int\:\frac{12}{(x^{2}-9)}dx
integral of (w^5)/(sqrt(8w^2+1))	\int\:\frac{w^{5}}{\sqrt{8w^{2}+1}}dw
tangent of f(x)=3x-2x^2,(-2,-14)	tangent\:f(x)=3x-2x^{2},(-2,-14)
(\partial)/(\partial x)(-6xy-x^6-y^6)	\frac{\partial\:}{\partial\:x}(-6xy-x^{6}-y^{6})
integral of 1/(6x+5)	\int\:\frac{1}{6x+5}dx
integral of 3x+3	\int\:3x+3dx
(y^4-x^2)((dy)/(dx))=-xy	(y^{4}-x^{2})(\frac{dy}{dx})=-xy
(dy)/(dt)=0.5-t+2y	\frac{dy}{dt}=0.5-t+2y
limit as x approaches 0 of (e/x)^x	\lim\:_{x\to\:0}((\frac{e}{x})^{x})

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