Solve: `(dy)/(dx)=sin^3x \ cos^4x+x\ sqrt(x+1)`

Explanation

`frac{d y}{d x}=sin ^{3} x cos ^{4} x+x sqrt{x+1}`


`Rightarrow d y=(sin ^{3} x cos ^{4} x+x sqrt{x+1}) d x`


Integrate both sides, of equation,


`int d y=int(sin ^{3} x cos ^{4} x+x sqrt{x+1}) d x `


`Rightarrow y=int sin ^{3} x cos ^{4} x d x+int x sqrt{x+1} d x `


`Rightarrow y=I_{1}+I_{2}` ………(1)


`I_{1}=int sin ^{3} x cos ^{4} x d x `


`I_{1}=int x sqrt{x+1} d x`


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