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Popular Calculus Problems

integral of xsin(9x^2)	\int\:x\sin(9x^{2})dx
derivative of (x^6/6+1/(16x^4))	\frac{d}{dx}(\frac{x^{6}}{6}+\frac{1}{16x^{4}})
limit as x approaches 0 of (sin(5x))/(sin(9x))	\lim\:_{x\to\:0}(\frac{\sin(5x)}{\sin(9x)})
integral of x(3x^2-5)	\int\:x(3x^{2}-5)dx
3x^2-2y^3(dy)/(dx)=0	3x^{2}-2y^{3}\frac{dy}{dx}=0
(\partial)/(\partial y)(x^2-y^2)	\frac{\partial\:}{\partial\:y}(x^{2}-y^{2})
integral of x^2+4x+3	\int\:x^{2}+4x+3dx
integral of (sec(x))/(1-tan(x))	\int\:\frac{\sec(x)}{1-\tan(x)}dx
derivative of (x^3-7(2x^2+3))	\frac{d}{dx}((x^{3}-7)(2x^{2}+3))
(sqrt(2x+4))^'	(\sqrt{2x+4})^{\prime\:}
integral from e to 4e of 1/x	\int\:_{e}^{4e}\frac{1}{x}dx
derivative of 12x\sqrt[3]{1-x}sqrt(x+1)	derivative\:12x\sqrt[3]{1-x}\sqrt{x+1}
integral from 0 to ln(3) of e^x-e^{-4x}	\int\:_{0}^{\ln(3)}e^{x}-e^{-4x}dx
(\partial)/(\partial y)(1+y^2sin(2x))	\frac{\partial\:}{\partial\:y}(1+y^{2}\sin(2x))
integral of x(1+x^2)	\int\:x(1+x^{2})dx
derivative of x^3-12x^2+45x	\frac{d}{dx}(x^{3}-12x^{2}+45x)
11x-4ysqrt(x^2+1)y^'=0,y(0)=2	11x-4y\sqrt{x^{2}+1}y^{\prime\:}=0,y(0)=2
derivative of e^{x/2} 1/2	\frac{d}{dx}(e^{\frac{x}{2}}\frac{1}{2})
derivative of y=x^2sin^4(x)+xcos^{-6}(x)	derivative\:y=x^{2}\sin^{4}(x)+x\cos^{-6}(x)
derivative of y= 9/(sqrt(x+8))	derivative\:y=\frac{9}{\sqrt{x+8}}
inverse oflaplace (s^2)/(s^4+2s^2+1)	inverselaplace\:\frac{s^{2}}{s^{4}+2s^{2}+1}
derivative of sqrt(2-7x)	derivative\:\sqrt{2-7x}
integral of 1/(x^2)-3/(x^4)	\int\:\frac{1}{x^{2}}-\frac{3}{x^{4}}dx
laplacetransform 2te^{3t}+4t^2e^{-5t}	laplacetransform\:2te^{3t}+4t^{2}e^{-5t}
derivative of 1/(sqrt(2x-3))	\frac{d}{dx}(\frac{1}{\sqrt{2x-3}})
derivative of 5-4x	derivative\:5-4x
taylor e^{x^5}	taylor\:e^{x^{5}}
integral of sin(x^2)	\int\:\sin(x^{2})dx
integral from 0 to infinity of e^{-3x}	\int\:_{0}^{\infty\:}e^{-3x}dx
integral from 0 to pi/6 of sin(3x)	\int\:_{0}^{\frac{π}{6}}\sin(3x)dx
derivative of sqrt((-x^3+10/4))	\frac{d}{dx}(\sqrt{\frac{-x^{3}+10}{4}})
integral of e^{2sin(3x)}cos(3x)	\int\:e^{2\sin(3x)}\cos(3x)dx
(\partial)/(\partial x)(2y^{1/2}x^{1/2})	\frac{\partial\:}{\partial\:x}(2y^{\frac{1}{2}}x^{\frac{1}{2}})
f(x)=(10)/x	f(x)=\frac{10}{x}
limit as x approaches 2 of (x^2)/(x^2-4)	\lim\:_{x\to\:2}(\frac{x^{2}}{x^{2}-4})
derivative of cos(xdx)	\frac{d}{dx}(\cos(x)dx)
integral of-4sin(2t-pi/2)	\int\:-4\sin(2t-\frac{π}{2})dt
derivative of (xtan(x)/(x^2+1))	\frac{d}{dx}(\frac{x\tan(x)}{x^{2}+1})
derivative of f(x)= 1/(2x+3)	derivative\:f(x)=\frac{1}{2x+3}
y^'+2/x y= 1/(x^2)	y^{\prime\:}+\frac{2}{x}y=\frac{1}{x^{2}}
derivative of (3x^2+2x-1/((1+3x^2)^2))	\frac{d}{dx}(\frac{3x^{2}+2x-1}{(1+3x^{2})^{2}})
y^'=2(t+1)y,y(0)=1	y^{\prime\:}=2(t+1)y,y(0)=1
y^{''}+2*y^'+y=e^{-t}	y^{\prime\:\prime\:}+2\cdot\:y^{\prime\:}+y=e^{-t}
sum from n=0 to infinity of 1/(2^nn!)	\sum\:_{n=0}^{\infty\:}\frac{1}{2^{n}n!}
derivative of f(x)=((x^3+1))/((x^4+1))	derivative\:f(x)=\frac{(x^{3}+1)}{(x^{4}+1)}
limit as x approaches-1 of (x+1)/(x^2-1)	\lim\:_{x\to\:-1}(\frac{x+1}{x^{2}-1})
integral of 2sqrt(4-x^2)	\int\:2\sqrt{4-x^{2}}dx
limit as x approaches pi of ((e^{sin(x)}-1))/(x-pi)	\lim\:_{x\to\:π}(\frac{(e^{\sin(x)}-1)}{x-π})
implicit (dy)/(dx),arctan(xy)=arcsin(2x+2y),(0,0)	implicit\:\frac{dy}{dx},\arctan(xy)=\arcsin(2x+2y),(0,0)
2ty^'-4y=4t^4e^{t^2}	2ty^{\prime\:}-4y=4t^{4}e^{t^{2}}
(\partial)/(\partial x)(4e^{5xy})	\frac{\partial\:}{\partial\:x}(4e^{5xy})
limit as x approaches+0 of 1/(csc(x))	\lim\:_{x\to\:+0}(\frac{1}{\csc(x)})
integral of 1/(100x^2+1)	\int\:\frac{1}{100x^{2}+1}dx
y^'= y/x+(6x^3)/y cos(x^2)	y^{\prime\:}=\frac{y}{x}+\frac{6x^{3}}{y}\cos(x^{2})
tangent of y=2x+x^2,(-2,0)	tangent\:y=2x+x^{2},(-2,0)
integral of x*x	\int\:x\cdot\:xdx
derivative of x/(x^2+100)	derivative\:\frac{x}{x^{2}+100}
f^'(x)=3x^2	f^{\prime\:}(x)=3x^{2}
integral of tan^3(9x)	\int\:\tan^{3}(9x)dx
derivative of pix(x-3)	\frac{d}{dx}(πx(x-3))
integral from-2pi to 2pi of pisin^2(x)	\int\:_{-2π}^{2π}π\sin^{2}(x)dx
integral of sec^3(1-4x)	\int\:\sec^{3}(1-4x)dx
y^{''}-10y^'+25y=0,y(0)=0,y^'(0)=3	y^{\prime\:\prime\:}-10y^{\prime\:}+25y=0,y(0)=0,y^{\prime\:}(0)=3
integral of xe^{-2x}	\int\:xe^{-2x}dx
integral of (x^2)/(x-7)	\int\:\frac{x^{2}}{x-7}dx
derivative of 1/(x^4-3/(x^2))	\frac{d}{dx}(\frac{1}{x^{4}}-\frac{3}{x^{2}})
derivative of (1-x/(1+sqrt(x)))	\frac{d}{dx}(\frac{1-x}{1+\sqrt{x}})
derivative of sqrt(x)(3x-2)	derivative\:\sqrt{x}(3x-2)
limit as x approaches infinity+of 1/x+x	\lim\:_{x\to\:\infty\:+}(\frac{1}{x}+x)
integral of (e^{5sqrt(t)})/(sqrt(t))	\int\:\frac{e^{5\sqrt{t}}}{\sqrt{t}}dt
(d^2y)/(dx^2)+64y=0	\frac{d^{2}y}{dx^{2}}+64y=0
(\partial)/(\partial x)(sqrt(1-x^7-y^7))	\frac{\partial\:}{\partial\:x}(\sqrt{1-x^{7}-y^{7}})
limit as θ approaches 0 of sin(θ)ln(θ)	\lim\:_{θ\to\:0}(\sin(θ)\ln(θ))
f(x)=(x^2-1)/x	f(x)=\frac{x^{2}-1}{x}
derivative of 15^x	\frac{d}{dx}(15^{x})
integral of xcos(2pi)x^2	\int\:x\cos(2π)x^{2}dx
limit as x approaches-6 of x	\lim\:_{x\to\:-6}(x)
derivative of sqrt(12+x)	\frac{d}{dx}(\sqrt{12+x})
limit as x approaches 0 of 1/(2xcsc(4x))	\lim\:_{x\to\:0}(\frac{1}{2x\csc(4x)})
limit as x approaches 0+of (x/(34))^x	\lim\:_{x\to\:0+}((\frac{x}{34})^{x})
integral from 0 to 16 of 1/(64-x^2)	\int\:_{0}^{16}\frac{1}{64-x^{2}}dx
y^3-(14x+4)+3xy^2y^'=0	y^{3}-(14x+4)+3xy^{2}y^{\prime\:}=0
y+y^4=(y^6+3x)(dy)/(dx)	y+y^{4}=(y^{6}+3x)\frac{dy}{dx}
derivative of y=(((3x^2))/((2x+4)))^3	derivative\:y=(\frac{(3x^{2})}{(2x+4)})^{3}
limit as x approaches 2+of 1	\lim\:_{x\to\:2+}(1)
integral of sqrt(x+\sqrt{x^2+2)}	\int\:\sqrt{x+\sqrt{x^{2}+2}}dx
derivative of x^3+x^2y^3-2y^2	\frac{d}{dx}(x^{3}+x^{2}y^{3}-2y^{2})
derivative of (4x^2+1^2)	\frac{d}{dx}((4x^{2}+1)^{2})
integral of 1/(x^4(x^2+3)^{1/2)}	\int\:\frac{1}{x^{4}(x^{2}+3)^{\frac{1}{2}}}dx
limit as x approaches 0+of e^{5/x}	\lim\:_{x\to\:0+}(e^{\frac{5}{x}})
derivative of (x^8-2^3)	\frac{d}{dx}((x^{8}-2)^{3})
(\partial)/(\partial x)(4y^3+2x^2y+1)	\frac{\partial\:}{\partial\:x}(4y^{3}+2x^{2}y+1)
(dy)/(dx)x+7y=e^{x^7}	\frac{dy}{dx}x+7y=e^{x^{7}}
integral of (ye^{x^2+y^2}+3y^2)	\int\:(ye^{x^{2}+y^{2}}+3y^{2})dy
derivative of (x^5/6+1/(10x^3))	\frac{d}{dx}(\frac{x^{5}}{6}+\frac{1}{10x^{3}})
derivative of f(x)=(2-3x-x^2)/(x^2-4)	derivative\:f(x)=\frac{2-3x-x^{2}}{x^{2}-4}
integral of (4x)/(x^2-1)	\int\:\frac{4x}{x^{2}-1}dx
y^{''}+4y^'=2x-3e^x	y^{\prime\:\prime\:}+4y^{\prime\:}=2x-3e^{x}
integral of 5cos^3(x)	\int\:5\cos^{3}(x)dx
derivative of 3/((2x-1^3))	\frac{d}{dx}(\frac{3}{(2x-1)^{3}})

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