What is the integral of 4sqrt(x)-7\sqrt[3]{x} ?

The integral of 4sqrt(x)-7\sqrt[3]{x} is 8/3 x^{3/2}-21/4 x^{4/3}+C

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integral of 4sqrt(x)-7\sqrt[3]{x}

\int 4 x - 7 3 x d x

\frac{8}{3} x^{\frac{3}{2}} - \frac{21}{4} x^{\frac{4}{3}} + C

Solution steps

\int 4 x - 7 3 x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 4 x d x - \int 7 3 x d x

\int 4 x d x = \frac{8}{3} x^{\frac{3}{2}}

\int 7 3 x d x = \frac{21}{4} x^{\frac{4}{3}}

= \frac{8}{3} x^{\frac{3}{2}} - \frac{21}{4} x^{\frac{4}{3}}

Add a constant to the solution

= \frac{8}{3} x^{\frac{3}{2}} - \frac{21}{4} x^{\frac{4}{3}} + C

\int 6 x^{2} \cdot arccos (x) d x

\int t 3 t - 4 d t

\int \frac{4 x - 6}{x ^{2} - 3 x + 7} d x

\int \frac{x ^{2} + 1}{x ^{4} + 10 x ^{3} + 21 x ^{2}} d x

\int + arctan (7 x) d x

What is the integral of 4sqrt(x)-7\sqrt[3]{x} ?
The integral of 4sqrt(x)-7\sqrt[3]{x} is 8/3 x^{3/2}-21/4 x^{4/3}+C